Claus Michael Ringel: Publications

The Library of Bielefeld University provides links to most of my publications (presently for the period 1970 - 1994),
see https://pub.uni-bielefeld.de/person/10583

List of publications (31.01.2013)


Annotated List of Publications since 2005

Some corrections     Additions

Manuscripts

Preprints

Accepted for publication

Published

[195] The short local algebras of dimension 6 with non-projective reflexive modules. (Nov 30, 2022, Jan 12, 2023).
arXiv:2211.16885
The paper was submitted to the journal Communications in Mathematics and Statistics,
and it was published there, however in a distorted version which was not endorsed by me. See volume 11(2): 195-227
In case you are interested, please look at the arXiv-version.

2022

[194] (with Pu Zhang) Gorenstein-projective modules over short local algebras (First version, Nov 19, 2019. Last revision June 1, 2022.)
arXiv:1912.02081
Journal of the London Mathematical Society, Volume 106, Issue 2 (2022), 528-589
http://dx.doi.org/10.1112/jlms.12577
[193] Linear Nakayama algebras which are higher Auslander algebras (April 29, 2021, completely revised Oct 13, 2021, revised June 14, 2022).
ID: 2077950 DOI:10.1080/00927872.2022.2077950
Communications in Algebra.
arXiv:2104.13806
[192] Are special biserial algebras homologically tame?
Algebras and Representation Theory.
Publication date: 2022-03-24
DOI 10.1007/s10468-022-10120-x, see pdf or epdf
A complement to the paper "Representation-tame algebras need not be homologically tame" (Algebras and Representation Theory 19, 2016) by Birge Huisgen-Zimmermann, see also her Banff-video

2021

[191] (with Pu Zhang) Koszul modules (and the Ω-growth of modules) over short local algebras
arXiv:1912.07512
Journal of Pure and Applied Algebra 225 (2021) 106772 https://doi.org/10.1016/j.jpaa.2021.106772
[190] The finitistic dimension of a Nakayama algebra
First version, August 23, 2020. The second part was changed completely. Final version: Jan 18, 2021, see arXiv:2008.10044
Journal of Algebra. https://doi.org/10.1016/j.jalgebra.2021.01.040
[189] Simple reflexive modules over finite-dimensional algebras.
Journal of Algebra and Its Applications (JAA), Vol. 20, Issue 09, Article 2150166 (2021).
DOI: 10.1142/S0219498821501668

2020

[188] (with Pu Zhang) On modules M such that both M and M* are semi-Gorenstein-projective.
Algebras and Representation Theory, 24(4) (2020), 1125-1140.
https://doi.org/10.1007/s10468-020-09982-w Link
[187] (with Pu Zhang) Gorenstein-projective and semi-Gorenstein-projective modules. II.
Journal of Pure and Applied Algebra. Vol 224, Issue 6, June 2020.
Article Number: 106248, https://doi.org/10.1016/j.jpaa.2019.106248
Link
[186] (with Pu Zhang) Gorenstein-projective and semi-Gorenstein-projective modules
Algebra & Number Theory. Vol. 14 (2020), No. 1, 1-36,   DOI: 10.2140/ant.2020.14.1

2018

[185] Kronecker modules generated by modules of length 2 (October 27, 2016, revised April 29, 2017).
Representations of Algebras. Contemp. Math. 705, Amer.Math.Soc. (296 pahes) (20. Mai 2018),
ISBN-10: 1470435764, ISBN-13: 978-1470435769, arXiv:1612.07679.
[184] The shift orbits of the graded Kronecker modules (Sept. 11, 2017, revised Feb 2. 2018)
Mathematische Zeitschrift, 290(3), 1199-1222, DOI 10.1007/s00209-018-2059-4
Online-first
[183] Quiver Grassmannians for wild acyclic quivers (March 26, 2017, version July 10, 2017).
Proceedings Amer.Math.Soc. vol 146 number 5, (2018), pages 1873-1877.
DOI: https://doi.org/10.1090/proc/13882   ISSN 1088-6826, 0002-9939.
Published electronically: January 16, 2018
[182] Chen-Ringel: Hereditary triangulated categories (June 27, 2016, final version: Feb 21, 2017)
Journal of Noncommutative Geometry. 12 (2018) 1 - 20. DOI 10.4171/JNGG/xxx.
(This replaces the old paper: Hereditary triangulated categories. Compositio Mathematica, to appear. SFB-Preprint 98-107)
[181] The root posets and their rich antichains (Jan 19, 2018) (in Chinese).
Scientia Sinica Mathematica 48/11. 1483-1506. doi: 10.1360/N012018-00015. (Special Issue for Professor Shaoxue Liu's 90th Birthday)
      This is an improved version of The (n-1)-antichains in a root poset of width n (Preliminary version, 2013).
      The appendix provides some visualization of the root posets which we could not find elsewhere.
      The pictures draw the attention to the fact that the root posets are locally distributive lattices
      which can be constructed using 3-dimensional cubes.

2017

[180] Lattice structure of torsion classe for hereditary artin algebras (Feb 6, 2014, version of Aug 7, 2016)
Nagoya J Math.
DOI: https://doi.org/10.1017/nmj.2017.12
Published online: 05 June 2017.
[179] The eigenvector variety of a matrix pencil. (Feb 23, 2017, revised: April 30, 2017)
Lin. Algebra and Appl. 531 (2017) 447-458. ISSN 0024-3795.
DOI: https://doi.org/10.1016/j.laa.2017.05.004
arXiv:1703.04097 (in math.NA)

2016

[178] Ringel-Zhang: Representations of quivers over the algebra of dual numbers (7.12.2011, revised version Nov 2016)
J. Algebra 475 (2016). 327-360. ISSN 0021-8693
DOI: 10.1016/j.jalgebra.2016.12.001
[177] The Catalan combinatorics of the hereditary artin algebras (Feb 23, 2015, 125 pages, revised August 24, 2015).
In: Recent Developments in Representation Theory, Contemp. Math., 673, Amer. Math. Soc., Providence, RI, (2016), 51-178 ISBN 978-1-4704-1955-4.
      The notes are based on the ICRA workshop lectures at Sanya, Hainan, and a related series of lectures at SJTU, Shanghai, given in August and September 2014.
[176] The representation theory of Dynkin quivers. Three contributions. (version July 2016)
In; Frontiers of Mathematics in China 11(4), 765-814. ISSN 1673-3452.
DOI 10.1007/s11464-016-0548-5 www.springer.com
      Part I of the paper is a revised version of The representations of a quiver of type An. A fast approach. (16.01.2013)
      Part II deals with the quivers of type Dn.
      Part III is devoted to the exceptional Dynkin cases,
      but also with the corresponding Euclidean quivers.
      We point out a relationship to the magic Freudenthal-Tits square
[175] Obaid, Nauman, Fakieh, Ringel:
The Ingalls-Thomas bijections
      (formerly the appendix of the first version of [173], revised version Feb 29, 2016)
IEJA vol 20 (2016), (ms #2515), ISSN 1306-6048.
[174] Obaid, Nauman, Fakieh, Ringel:
Static subcategories of the module category of a finite-dimensional hereditary algebra. (19.7.2014, slightly revised April 9, 2015)
Comm. Algebra. Volume 44, Issue 6 (2016) pages 2531-2546. ISSN 0092-7872
DOI: 10.1080/00927872.2015.1053902
Paper

2015

[173] Obaid, Nauman, Fakieh, Ringel: The numbers of support-tilting modules for Dynkin algebras. (24.3.2014, revised version Sept 18, 2015)
Journal of Integer Sequences, Vol. 18 (2015), Article 15.10.6
[172] Ringel-Zhang: Objective triangle functors
Sci China Math, 2015, 58: 221-232, doi: 10.1007/s11425-014-4954-4
SCM

2014

[171] Generic representations of wild quivers.
Int Math Res Notices (2014). doi: 10.1093/imrn/rnu224
[170] Ringel-Zhang: From submodule categories to preprojective algebras
Math Z. 278 (2014), 55-73. DOI: 10.1007/s00209-014-1305-7
[169] Quiver Grassmannians and Auslander varieties for wild algebras (17.05.2013, revised 20.05.2013)
J.Algebra 402 (2014), 351-357.
DOI: 10.1016/j.jalgebra.2013.12.021

2013

[168] Obaid, Nauman, Shammakh, Fakieh, Ringel: The number of complete exceptional sequences for a Dynkin algebra
(first version July 29, 2013, revised Nov 23, 2013)
Colloq. Math. 133 (2013), 197-210
[167] The Auslander bijections: How morphism are determined by modules
Bull. Math. Sci. 3 (2013), no. 3, 409.484.
[166] The Gorenstein projective modules for the Nakayama algebras. I.
Journal of Algebra (2013), pp. 241-261. DOI 10.1016/j.jalgebra.2013.03.014
[165] Indecomposable representations of the Kronecker quivers
Proc. Amer. Math. Soc. 141 (2013), no. 1, 115.121.
(MR2988715)
[164] Distinguished bases of exceptional modules
In "Algebras, quivers and representations". Proceedings of the Abel symposium 2011. Springer Series Abel Symposia Vol 8. (2013) 253-274.

2012

[163] Morphisms determined by objects: The case of modules over artin algebras (31.10.2011, final revision 14.01.2013)
Illinois Journal of Mathematics 56 (2012), 981-1000.
A correction
[162] Ringel-Xiong: On radical square zero rings.
Algebra and Discrete Mathematics. Volume 14 (2012), 297 - 306.
[161] Cluster-additive functions on stable translation quivers
J. Algebraic Combin. 36 (2012), no. 3, 475.500.
DOI 10.1007/s10801-012-0346-4. link
[160] Minimal infinite cogeneration-closed subcategories.
Bull. Sci. math. 136 (2012), pp 820-830. DOI: 10.1016/j.bulsci.2012.03.002
      This incorporates (at least partly) the ms
      Take-off subcategories: Any infinite cogeneration-closed subcategory contains a minimal infinite cogeneration closed subcategory.
      (Selected topics, 21.06.2006) as well as
      Pillars
      (Selected topics, 31.05.2006)
[159] Fahr-Ringel: The Fibonacci partition triangles.
Advances in Mathematics 230 (2012), pp. 2513-2535 DOI information: 10.1016/j.aim.2012.04.010
      Rejected by JIS (Journal of Integer Sequences) as follows: the referee (who is an expert in integer sequences and represents the target audience for our Journal) couldn't really understand the point and objected to the specialized terminology (quiver, pylon, etc.).
[158] On the representation dimension of artin algebras
Bulletin of the Institute of Mathematics, Academia Sinica, vol 7 (1) (2012), p.33-70.
In: Proceedings of the Taipei Conference on Representation Theory held in Taipei in 2010. Link
Bulletin of the Institute of Mathematics, Academia Sinica, volume 6 number 4 (2011), volume 7 number 1 (2012), volume 7 number 2 (2012).
[157] Fahr-Ringel: Categorification of the Fibonacci Numbers Using Representations of Quivers
Journal of Integer Sequences. Vol. 15 (2012), Article 12.2.1 Reprint

2011

[156] The minimal representation-infinite algebras which are special biserial
In: Representations of Algebras and Related Topics,
EMS Series of Congress Reports, European Math. Soc. Publ. House, Zürich, 2011
(Editors Andrzej Skowronski and Kunio Yamagata), p.501-560.
[155] Indecomposables live in all smaller lengths
Bull. London Math. Soc. (2011) 43(4): 655-660,   doi: 10.1112/blms/bdq128
Reprint
[154] The SL3-module T(43) for p=3
An appendix to the paper: Decomposition of tensor products of modular representations of SL_3 by Bowman, Doty, Martin.
International Electronic Journal of Algebra 9 (2011), 177-219
Final version
[153] Cluster-concealed algebras
Advances in Mathematics. 226, (2011), Pages 1513-1537

2010

[152] Gabriel-Roiter inclusions and Auslander-Reiten theory (Nov 1, 2009, slightly revised Aug 20, 2010).
Journal of Algebra 324 (2010) 3579-3590
[151] Iyama's finiteness theorem via strongly quasi-hereditary algebras (September 29, 2009)
Journal of Pure and Applied Algebra 214 (2010) 1687-1692. article
The published version contains a lot of misprints - due to incorrect conversion from TeX to LaTeX. Thus, use the preprint version!

Corrections

    Remarks: For the first proposition in A2, see Theorem 3 in [76] Dlab-Ringel: Filtrations of right ideals related to projectivity of left ideals. SLNM 1404 (1989), 95-107.

    This paper also contains further conditions which are equivalent to being strongly quasi-hereditary, see Theorem 2.

    Also, in this paper, as well as in Dlab-Ringel [77] it is shown that starting with any species without loops, one may construct algebras which are both left and right strongly quasi-hereditary with this species, namely the "deep algebras" ([77]) and the "peaked algebras" ([76]).

2009

[147] The relevance and the ubiquity of Prüfer modules.
Proceedings of the 4th International Conference on Representation Theory (edt: Zongzhu Lin, Jianpan Wang). Contemporary Mathematics. Amer. Math. Soc. 478 (2009), 163-176 ISBN-10: 0-8218-4555-1, ISBN-13: 978-0-8218-4555-4
pdf

2008

[150] The first Brauer-Thrall conjecture.
In: Models, Modules and Abelian Groups. In Memory of A. L. S. Corner. Walter de Gruyter, Berlin (edt: B. Goldsmith, R.Göbel) (2008), 369-374.
pdf
[149] (with V.Dlab): The global dimension of the endomorphism ring of a generator-cogenerator for a hereditary artin algebra.
Mathematical Reports of the Academy of Science of the Royal Society of Canada. Vol 30 (2008), Nr.3, 89-96.
pdf, Published version: pdf
[148] The self-injective cluster tilted algebras.
Archiv der Mathematik. Band 91 (2008) Nr.3, 218-225.
pdf. (14.05.2008)
[146] (with M. Schmidmeier) Invariant subspaces of nilpotent operators. I.
Journal Reine Angew. Math. Band 2008, Nr. 614 (2008), 1--52.
Preprint or ArXiv math.RT/0608666
    Correction: On page 3, between (0.1.3) and (0.1.4), the subspace Uc is supposed to be generated by the three elements mentioned and their images under powers of T.
[145] (with M. Schmidmeier) The Auslander-Reiten Translation in Submodule Categories.
Trans. Amer. Math. Soc. 360 (2008), 691-716.
pdf-file.
[144] (with Ph. Fahr): A partition formula for Fibonacci numbers.
Journal of Integer Sequences, Vol. 11 (2008), Article 08.1.4.
pdf
Correction: Page 1, line -10: replace "the preprojective" by "preprojective" - one gets in this way only one τ-orbit of the preprojectives, not all!

2007

[143] The ladder construction of Prüfer modules.
Revista de la Union Matematica Argentina. (2007) Vol 48-2, p.47-65. volume 48
pdf
[142] Some remarks concerning tilting modules and tilted algebras.
Origin. Relevance. Future.
(An appendix to the Handbook of Tilting Theory.)
(ed Angeleri Hügel, Happel, Krause), London Math. Soc. Lecture Note Series vol 332. Cambridge University Press (2007). ISBN-13: 9780521680455, p.413-472.
pdf-file (Final version, May 2006)
Remark

2006

[141] The theorem of Bo Chen and Hall polynomials.
Nagoya Journal vol 183 (2006), 143-160.
pdf-file
[140] Algebras, Rings And Their Representations:
Proceedings Of The International Conference on Algebras, Modules and Rings, Lisbon, Portugal, 14-18 July 2003 (ed Facchini, Fuller, Ringel, Santa-Clara).
World Scientific Publishing Company (2006), 371 pages.
ISBN-10: 9812565981
[139] Foundation of the Representation Theory of Artin Algebras, Using the Gabriel-Roiter Measure.
In: Trends in Representation Theory of Algebras and Related Topics. (Workshop Queretaro, Mexico, 2004). Edited by de la Pena and Bautista. Contemporary Math. 406. Amer.Math.Soc. (2006), 105-135.
(Including a remark that one should be concerned about the military involvement of the publisher of the volume, the American Mathematical Society).
pdf-file. (22.04.2006)
(This version combines my Hirosaki-notes 2003, notes for the Hangzhou lectures 2005 and some additional considerations.)

[138] (with M. Schmidmeier) Submodule categories of wild representation type.
Journal for Pure and Applied Algebra 205, Issue 2, May 2006, Pages 412-422.
dvi-file, as ps-file, as pdf-file.
math.RT/0409417
[137] (with I. Reiten) Infinite dimensional representations of canonical algebras.
Canadian Journal of Mathematics 58 (2006), 180-224.
pdf-file with an Appendix: Cotorsion pairs: dvi-file, as ps-file, as pdf-file,

2005

[136] The Gabriel-Roiter measure.
Bull. Sci. math. 129 (2005), 726-748.
(Bei den Commentarii Math Helv eingereicht, aber nicht angenommen - weil es keine Originalarbeit sei). dvi-file, as ps-file. as pdf-file
[135] Bautista and the Development of the Representation Theory of Artin Algebras
Proceedings XV Latinamerican Colloquium of Algebra.
Contemporary Mathematics 376. Amer.Math.Soc.(2005), 89-103.
dvi-file, as pdf-file.
      On Sept 20, 2013, P. Gabriel sent me a long letter, accusing me of "punishable cybermobbing" and requesting to replace the section "Multiplicative Bases" by a version written by him. (for example, my formulation Gabriel was furious about this commment (p.5, lines 17/18) is replaced by Gabriel complained about this comment, and so on - but really, when he phoned me, he was furious ...).

      On Aug 5, 2015, I obtained a message from R. Bautista, asking me to add a note in order to clarify the cooperation of the authors.

      See also Gabriel: About Teamwork, and see also the linked pages Timing and Rectifications

      Remark: The statement "About Teamwork" starts with the following formulation:
      Teamwork requires the observation of a minimal amount of rules: a) Statements or proofs within a team-publication, which are not explicitly attributed to a specified member, belong to the whole team; b) Concerning the internal team-work, the members are bound to an amount of discretion avoiding cacophony.

      But the dispute between Gabriel and me concerns the time before the cooperation between Gabriel on the one hand and Bautista, Roiter and Salmeron on the other hand, had started.

      The controversy concerns the fact that in [BGRS] the main result, the existence of a multiplicative basis, is contributed to Roiter, whereas it was known that Roiter did not have a complete proof.

      I myself refer to this assertion as "theorem of Roiter and Bautista", since I was present when Bautista presented his proof at UNAM, spring 1983. This proof completed the arguments of Roiter (Bautista acknowledged contributions by Salmeron, thus one may question whether one should also refer to him). It is decisive to stress that this presentation was before the cooperation with Gabriel even had started.


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Fakultät für Mathematik, Universität Bielefeld
Verantwortlich: C.M.Ringel
E-Mail: ringel@mathematik.uni-bielefeld.de
Aug 24, 2015