The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form.
Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a …

A module is extending (or CS, C1) if every complement submodule is a direct summand or,
equivalently, every submodule is essential in a direct summand. The terms extending and …

This unique and comprehensive volume provides an up-to-date account of the literature on
the subject of determining the structure of rings over which cyclic modules or proper cyclic …

Quasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. Since
then, these classical artinian rings have continued to fascinate ring theorists with their …

Following the concept of generalized small submodule, we define $ g $-supplemented
modules and characterize some fundamental properties of these modules. Moreover, the …

A module M is called ss-supplemented if every submodule U of M has a supplement V in M
such that U (intersection) V is semisimple. It is shown that a finitely generated module M is ss …

A module M is called a D 4-module if, whenever A and B are submodules of M with M= A⊕
B and f: A→ B is a homomorphism with Im f⊆⊕ B, we have ker f⊆⊕ A. The class of D 4 …

Motivated by a relation on submodules of a module used by both AW Goldie and PF Smith,
we say submodules X, Y of M are β* equivalent, Xβ* Y, if and only if is small in and is small …

In this paper we introduce-non-cosingular modules, dual Baer modules and-modules. We
prove that a module M is lifting and-non-cosingular if and only if it is a dual Baer and …

Let R be an arbitrary ring. A nonzero unital right R-module M is called a second module if M
and all its nonzero homomorphic images have the same annihilator in R. It is proved that if R …