Claus Michael Ringel

Annotated List of Publications 1970 - 1988

• [1] Eine Charakterisierung der Homotopiekategorie der CW-Komplexe. Math. Z. 115 (1970), 359-365.
• [2] Diagonalisierungspaare I, Math. Z. 117 (1970), 249-266.
• [3] Diagonalisierungspaare II, Math. Z. 122 (1971), 10-25.
• [4] Faserungen und Homotopie in Kategorien. Math. Ann. 190 (1971), 215-230.
• [5] Monofunctors as reflectors. Trans. Amer. Math. Soc. 161 (1971), 293-306.
• [6] (mit V. Dlab) Anneaux balanc\'es. C.R. Acad. Sc. Paris A 272, (1971), 1555-1558.
• [7] The intersection property of amalgamations. J. Pure Appl. Algebra 2 (1972), 341-342.
• [8] (mit H. Herrlich) Identities in categories. Can. Math. Bull. 15 (1972), 297-299.
• [9] (mit V. Dlab) Rings with the double centralizer property. J. Algebra 22 (1972), 480-501.
• [10] (mit V. Dlab) A class of balanced non-uniserial rings. Math. Ann. 195 (1972), 279-291.
  (A conterexample to a conjecture of Jans (Math. Ann. 188 (1970).)
• [11] (mit V. Dlab) Balanced local rings with commutative residue fields. Bull. Amer. Math. Soc. 78 (1972), 771-774.
• [12] (mit V. Dlab) Balanced rings. In: Lectures on Rings and Modules. Springer LNM 246 (1972), 73-143.
• [13] (mit V. Dlab) Decomposition of modules over right uniserial rings. Math. Z. 129 (1972), 207-230.
• [14] (mit V. Dlab) The structure of balanced rings. Proc. London Math. Soc. (3) 26 (1973), 446-462.
• [15] (mit V. Dlab) Exceptional rings. Coll. Math. Soc. J. Bolyai 6. Rings, Modules and Radicals. Keszthely (Hungary) 1971, (1973), 167-171.
• [16] (mit V. Dlab) A construction of rings whose injective hull is a ring. Austr. J. Math. 16 (1973), 7-13.
• [17] Socle conditions for QF-1 rings. Pacific J. Math. 44 (1973), 309-336.
• [18] QF-1 rings of global dimenseion $\le 2$. Canad. J. Math. 25 (1973), 345-352.
• [19] (mit V. Dlab) Repr\'esentations indecomposables des alg\`ebres. C.R. Acad. Sc. Paris A 276 (1973), 1393-1396.
• [20] (mit V. Dlab) Sur la conjecture de Brauer-Thrall, C.R. Acad. Sc. Paris A 276 (1973), 1441-1442.
• [21] Commutative QF-1 rings. Proc. Amer. Math. Soc. 42 (1974), 365-368.
• [22] (mit H. Tachikawa) QF-3 rings. J. Reine Angew. Math. 272 (1975), 49-72.
• [23] (mit V. Dlab) On algebras of finite representation type. J. Algebra 33 (1975), 306-394.
• [24] (mit V. Dlab) Repr\'esentations des graphes valu\'es. C.R. Acad. Sc. Paris A 278 (1975), 537-540.
• [25] Unions of chains of indecomposable modules. Comm. Algebra 3 (1975), 1121-1144.
• [26] The indecomposable representations of the dihedral 2-groups. Math. Ann. 214 (1975), 19-34.
• [27] The representation type of local algebras. Proc. ICRA 1974. Springer LNM 488 (1975), 282-305.
• [28] (mit V. Dlab) Indecomposable representations of graphs and algebras. Mem. Amer. Math. Soc. 173 (1976).
• [29] Representations of K-species and bimodules. J. Algebra 41 (1976), 269-302.
• [30] (mit S. Brenner) Pathological modules over tame rings. J. London Math. Soc. 14 (1976), 207-215. Remark
• [31] (mit V. Dlab) Normal forms of real matrices with respect to complex similarity. Linear Alg. and Appl. 17 (1977), 107-124.
• [32] (mit V. Dlab) Real subspaces of a quaternion vector space. Canad. J. Math 30 (1978), 1228-1242.
• [33] (mit S. J\o ndrup) Remarks on a paper by Skornjakov concerning rings for which every module is a direct sum of left ideals. Archiv Math. 31 (1978), 329-331.
• [34] (mit V. Dlab) The representations of tame hereditary algebras. Proc. Philadelphia Conf. 1976. Marcel Dekker (1978), 329-353.
• [35] Finite-dimensional hereditary algebras of wild representation type. Math. Z. 161 (1978), 235-255.
• [36] (mit V. Dlab) A module theoretic interpretation of properties of the root systems. Proc. Conf. Ring Theory Antwerp 1978. Marcel Dekker Lecture Notes Pure Appl. Math 51 (1979), 435-451.
• [37] Infinite dimensional representations of finite dimensional hereditary algebras. Symposia Math. 23 (1979), 321-412.
  Corrections
• [38] The spectrum of a finite dimensional algebra. Proc. Conf. Ring Theory Antwerp 1978. Marcel Dekker Lecture Notes Pure Appl. Math 51 (1979), 535-797.
• [39] (mit K.W. Roggenkamp) Indecomposable representations of orders and Dynkin diagrams. C.R. Acad. Sci. Canada 1 (1979), 91-94.
• [40] (mit K.W. Roggenkamp) Diagrammatic methods in the representation theory of orders. J. Algebra 60 (1979), 11-41.
• [41] (mit K.W. Roggenkamp) Socle determined categories of representations of artinian hereditary algebras. J. Algebra 64 (1980), 249-269.
• [42] (mit V. Dlab) A remark on normal forms of matrices. Linear Alg. and Appl. 30 (1980), 109-114.
• [43] (mit V. Dlab) Perfect elements in the free modular lattices. Math. Ann. 247 (1980), 95-100.
• [44] (mit V. Dlab) The preprojective algebra of a modulated graph. Proceedings ICRA 2. Springer LNM 832 (1980), 216-231.
• [45] (mit P. Dowbor, D. Simson) Hereditary artinian rings of finite representation type. Proceedings ICRA 2. Springer LNM 832 (1980), 232-241.
• [46] (mit D. Happel, U. Preiser) Vinberg's characterization of Dynkin diagrams using subadditive functions with application to DTr-periodic modules. Proc. ICRA 2. Springer LNM 932 (1980), 280-294.
• [47] (mit D. Happel, U. Preiser) Binary polyhedral groups and Euclidean diagrams. Manuscripta math. 31 (1980), 317-329.
• [48] Reflection functors for hereditary algebras. J. London Math. Soc. (2) 21 (1980), 465-479.
• [49] The rational invariants of tame quivers. Invent. Math. 58 (1980), 217-239.
• [50] Report on the Brauer-Thrall conjectures. Proceedings ICRA 2. Springer LNM 831 (1980), 104-136.
  The third part of this report is faulty. in particular, I am not aware about a proof of Proposition 3.1.
      When writing the report, I was fascinated by the work of Nazarova and Roiter, and tried to generalize the main ideas to base fields which are not necessarily algebraically closed. However, it turned out that already the NR treatment for algebraically closed base fields is incomplete. There were additions by Nazarova and Roiter as well as by Gabriel, provided for the ICRA proceedings 1984 (they are available in the Carleton Notes) which aimed to close the gaps. However, several counter examples were found, thus these additions were not incorporated into the corresponding Springer LNM volume 1177. At present, no proof of BTh II along the lines of NR is known. Of course, this also means that my attempt to generalize this approach to general fields failed.
• [51] Tame algebras. Proceedings ICRA 2. Springer LNM 831 (1980), 137-287.
• [52] (mit V. Dlab) Eigenvalues of Coxeter transformations and the Gelfand-Kirillov-dimension of preprojective algebras. Proc. Amer. Math. Soc. 83 (1981), 228-232.
• [53] Kawada's theorem. Proceedings Oberwolfach Conf. Abelian Groups. Springer LNM 874 (1981), 431-446.
• [54] (mit D. Happel) Construction of tilted algebras. Proceedings ICRA 3. Springer LNM 903 (1981), 125-167.
• [55] (mit K. Bongartz) Representation-finite tree algebras. Proceedings ICRA 3. Springer LNM 903 (1981), 39-54.
• [56] Four papers on linear algebras. Vorwort zu: Representation theory. Selected papers by I.M. Gelfand et al. London Math. Soc. LN Series 69 (1982), 141-156.
• [57] (mit D. Happel) Tilted algebras. Trans. Amer. Math. Soc. 274 (1982), 399-443.
• [58] Unzerlegbare Darstellungen endlich-dimensionaler Algebren. Jber. d. Dt. Math. Verein. 85 (1983), 86-105.
• [59] Bricks in hereditary length categories. Resultate der Math. 6 (1983), 64-70.
• [60] Separating tubular series. Sem. Malliavin. Springer LNM 1029 (1983), 134-158.
• [61] (mit G. d'Este) Coherent tubes. J. Algebra 87 (1984), 150-201.
• [62] Tame algebras and integral quadratic forms. Springer LNM 1099 (1984).
• [63] Indecomposable representations of finite dimensional algebras. Proceedings International Conference of Mathematicians. Warszawa 1983, (1984), 425-436.
• [64] (mit V. Dlab) A class of bounded hereditary noetherian domains. J. Algebra 92 (1985), 311-321.
• [65] (mit D. Happel) The derived category of a tubular algebra. Proceedings ICRA 4. Springer LNM 1177 (1986), 156-180.
• [66] Representation theory of finite dimensional algebras. Durham Lectures 1985. London Math. Soc. Lecture Note Series 116 (1986), 7-79.
• [67] (mit D. Vossieck) Hammocks. Proc. London Math. Soc. (3) 54 (1987), 216-246.
  Corrections
• [68] (mit M.C.R. Butler) Auslander-Reiten sequences with few middle terms, with applications to string algebras. Comm. Algebra 15 (1987), 145-179.
• [69] The regular components of the Auslander-Reiten quiver of a tilted algebra. Chinese Ann. Math. B. 9 (1988), 1-18.
• [70] (mit E. Marmolejo) Modules of bounded length in Auslander-Reiten components. Archiv Math. 50 (1988), 128-133.