Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

In this article, we study the second radical of a module over an arbitrary ring R as the dual
notion of the prime radical of a module. We give some properties of the second radical and …

Book Journal 2009 V8/1.indb Page 1 CMU. J. Nat. Sci. (2009) Vol. 8(1) S 105 Strong
Comultiplication Modules H. Ansari-Toroghy* and F. Farshadifar Department of Mathematics …

Let R be a ring, M be a left R-module and Spec (RM) be the collection of all prime
submodules of M. In this paper and its sequel, we introduce and study a generalization of …

It is proved that if R is a right FBN ring then a non-zero right R-module M has the property
that HomR (M, N)≠ 0 for every non-zero submodule N of M if and only if HomR (M, R/P)≠ 0 …

In this article, we introduce and study a generalization of the classical Krull dimension for a
module MR. This is defined to be the length of the longest strong chain of prime submodules …

Let R be a commutative ring with identity, S a multiplicatively closed subset of R, and M be
an R-module. The aim of this article is to introduce and investigate some properties of the …

S-second submodules of a module Page 1 © Algebra and Discrete Mathematics RESEARCH
ARTICLE Volume 32 (2021). Number 2, pp. 197ś210 DOI:10.12958/adm1437 S-second …

R denotes a commutative ring. After Bass [B], a ring R is perfect in case every module has a
projective cover. A ring R is a max ring provided that every nonzero i2-module has a …

All rings are assumed to be associative and (except for nil-rings and some stipulated cases)
to have nonzero identity elements. Expressions such as a “Noetherian ring” mean that the …