A theorem due to Nakayama and Skornyakov states that “a ring R is an Artinian serial ring if
and only if all left R-modules are serial” and a theorem due to Warfield state that “a …

A result of Nakayama and Skornyakov states that a ring R is an Artinian serial ring if and
only if every R-module is serial. This motivated us to study commutative rings for which every …

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 …

Nakayama, who called these rings generalized uniserial rings, proved [21, Theorem 171
that every finitely generated module over a serial ring is a direct sum of uniserial modules. In …

In this paper we shall characterize the generators whose endomorphism rings are serial
Noetherian. A module is serial when its submodules are linearly ordered with respect to …

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 module M is called uniserial if the set of submodules of M is linearly ordered by inclusion.
A ring R is called right serial if RR is a direct sum of uniserial modules. Left serial rings are …

Since any right artinian ring with identity is right noetherian, this theorem generalizes the
classical Wedderburn-Artin theorem which states that a right artinian simple ring with identity …

We define prime uniserial modules as a generalization of uniserial modules. We say that an
R-module M is prime uniserial (℘-uniserial) if its prime submodules are linearly ordered by …

We study the class of virtually uniserial modules and rings as a nontrivial generalization of
uniserial modules and rings. An R-module M is virtually uniserial if for every finitely …