A well known result by Osofsky (1964) states that if over a ring R every cyclic right module is
injective, then R is semi-simple artinian. This has motivated the study of rings over which …

A theorem of Cartan-Eilenberg (Cartan, H., Eilenberg, S.(1956). Homological Algebra.
Princeton: Princeton University Press, pp. 390.) states that a ring R is right Noetherian iff …

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 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 …

6 0 GOEL AND JAIN self-injective ring (or if R is a semiperfect ring) then each cyclic R-
module is a-injective if and only if R is a direct sum of semisimple artinian ring and a finite …

The fundamental result of the paper is Theorem I, asserting that over a right Noetherian ring
R, the poor injectivity of all cyclic modules is equivalent to the fact that R is a direct sum of a …

A well-known result of Osofsky [10, 11] states that a ring R is semisimple artinian iff every
cyclic R-module is injective. From this it follows that a right self-injective right hereditary ring …

In [2, Thm. 1.2] Eisenbud and Griffith showed that a right perfect ring with only finitely many
isomorphism classes of cyclic indecomposable left modules is left artinian. Without the …

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) …

The object of this paper is to prove Theorem. For a ring $ R $ the following are equivalent:(i)
Every cyclic right $ R $-module is injective or projective.(ii) $ R= S\oplus T $ where $ S $ is …