A famous theorem of algebra due to Osofsky states that “if every cyclic left R-module is
injective, then R is semisimple”. Therefore, a natural question of this sort is:“What is the class …

A well-known result of Köthe and Cohen-Kaplansky states that “a commutative ring R has
the property that every R-module is a direct sum of cyclic modules if and only if R is an …

A theorem from commutative algebra due to Köthe and Cohen-Kaplansky states that,“a
commutative ring R has the property that every R-module is a direct sum of cyclic modules if …

In [20, 21], Osofsky showed that a ring all of whose cyclic modules are injective is
semisimple Artinian. Since that time, a cyclic, finitely presented module version of the …

Rings Whose Modules Are {oplus}-Supplemented Page 1 Ž . Journal of Algebra 218, 470487
1999 Article ID jabr.1998.7830, available online at http:rrwww.idealibrary.com on Rings Whose …

Recall that an R-module M is pure-semisimple if every module in the category σ [M] is a
direct sum of finitely generated (and indecomposable) modules. A theorem from …

AN AFFIRMATIVE ANSWER TO A QUESTION ON NOETHERIAN RINGS Page 1 January 31,
2008 12:6 WSPC/171-JAA 00263 Journal of Algebra and Its Applications Vol. 7, No. 1 (2008) …

A characterization of noetherian rings by cyclic modules Page 1 Proceedings of the Edinburgh
Mathematical Society (1996) 39, 253-262 I A CHARACTERIZATION OF NOETHERIAN RINGS …

For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for
every cyclic right module N. The rings whose simple-injective right modules are injective are …

Theorem (K6the-Cohen-Kaplansky). A commutative ring R has the property that each of its R-
modules is a direct sum of cyclic modules if and only if R is an artinian principal ideal ring …