ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16 Rizvi, S. Tariq, The Ohio State University, Lima, U. S. A. On noetherian and artinian rings. We investigate rings with special module decompositions M = P ⊕Q where P is projective and Q has some special properties. We obtain a new characterization of noetherian rings: A ring R is right noetherian if and only if every cyclic right R-module is a direct sum of a projective module P and a module Q where Q is either injective or noetherian. A module is called CS (or extending) if every submodule is essential in a direct summand. We also investigate rings R for which every (countably generated) right R-module is a direct sum of a projective module P and a CS /quasi-continuous module Q. These provide classes of right artinian rings with “nice” properties. (This is a part of joint work with D. V. Huynh.)