Preface All rings are assumed to be associative and (except for nilrings and some stipulated cases) to have nonzero identity elements. A ring A is said to be regular if for every element a E A, there exists an element b E A with a = aba. Regular rings are well studied. For example, 163] and 350] are devoted to regular rings. A ring A is said to be tr-regular if for every element a E A, there is an element n b E A such that an = anba for some positive integer n. A ring A is said to be strongly tr-regular if for every a E A, there is a positive integer n with n 1 n an E a + An Aa +1. It is...
Preface All rings are assumed to be associative and (except for nilrings and some stipulated cases) to have nonzero identity elements. A ring A is sai...
This is the first monograph on rings closed to von Neumann regular rings. The following classes of rings are considered: exchange rings, pi-regular rings, weakly regular rings, rings with comparability, V-rings, and max rings. Every Artinian or von Neumann regular ring A is an exchange ring (this means that for every one of its elements a, there exists an idempotent e of A such that aA contains eA and (1-a)A contains (1-e)A). Exchange rings are very useful in the study of direct decompositions of modules, and have many applications to theory of Banach algebras, ring theory, and K-theory....
This is the first monograph on rings closed to von Neumann regular rings. The following classes of rings are considered: exchange rings, pi-regular...
This is monograph on the theory of semidistributive modules and rings investigates such topics as the relationship between semidistributive modules and flat, projective, injective, multiplication, as well as Bezout modules.
This is monograph on the theory of semidistributive modules and rings investigates such topics as the relationship between semidistributive modules an...
