This volume provides a comprehensive introduction to module theory and the related part of
ring theory, including original results as well as the most recent work. It is a useful and …

EINLEITUNG. Auf die Frage nach einer Charakterisierung derjenigen Familien (Mk) keK von
Moduln Uber einem Ring R, deren direkte Summe 8 M im Produkt 1 Mk k€ K kk€ K …

Let 𝑅 be a commutative ring with identity. A unital 𝑅-module 𝑀 is a comultiplication module
provided for each submodule 𝑁 of 𝑀 there exists an ideal 𝐴 of 𝑅 such that 𝑁 is the set of …

Let p be a prime, and k be a field of characteristic p. We investigate the algebra structure and
the structure of the cohomology ring for the connected Hopf algebras of dimension p 3 …

IYTRODCCTION 1: n~ onorphism rings of various types of modules have been objects of
extensive study in the recent past [2, 11, 14, 15, 18, 25, 261. In [15] Erika Mares introduced …

Modules whose nonzero endomorphisms are epimorphisms and modules whose nonzero
endomorphisms are monomorphisms are considered in this paper. We prove that these two …

Cukerman [2], Shanny [5], and Ware [7] have shown that a ring R is Artin semisimple if and
only if R has a nonfinitely generated free module with regular endomorphism ring. This …

Let and be rings. The objective is to study the bimodule satisfying the annihilator conditions
for all. This approach will clearly show how the ring or the module is connected to the …

As is well known, each endomorphism of an Artinian, Noetherian and indecomposable
module is either nilpotent or anautomorphism. CI Vin-sonhaler has proved that each …

Let R be a commutative Noetherian integral domain with field of fractions Q. Generalizing a
forty-year-old theorem of E. Matlis, we prove that the R-module Q/R (or Q) has Krull …