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 …

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

The great challenge in writing a book about a topic of ongoing mathematical research
interest lies in determining who and what. Who are the readers for whom the book is …

An associative ring R with identity is semiperfect if and only if every element of R is a sum of
a unit and an idempotent, and R contains no infinite set of orthogonal idempotents. A ring …

It is shown that if e is an idempotent in a ring R such that both eRe and (1− e) R (1− e) are
clean rings, then R is a clean ring. This implies that the matrix ring M n (R) over a clean ring …

An element a of a ring R is nil-clean if a= e+ b where e 2= e∈ R and b is a nilpotent; if further
eb= be, the element a is called strongly nil-clean. The ring R is called nil-clean (resp …

We systematically study rings whose units are all unipotent. The first main result is that a ring
R has this property if and only if R has a 2-power characteristic and the unit group of R is a …

This article concerns mainly on various ring properties of Morita contexts. Necessary and
sufficient conditions are obtained for a general Morita context or a trivial Morita context or a …

In the present note, we continue the study of skew inverse Laurent series ring R ((x− 1; α, δ))
and skew inverse power series ring R [[x− 1; α, δ]], where R is a ring equipped with an …

A ring R is called to be exchange if the right regular module RR has finite exchange
property. We continue in this paper the study of exchange rings by several authors. In …