Various types of “divisibility” have been considered in the literature [5, 12J all of which make
injective modules “divisible.” IUore recently: Wei [19] introduced a divisibility in terms of the …

A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal
has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple …

К настоящему времени найдены многочисленные критерии квазифробениусовости
кольца (см., например,[2],[3],[8]—[10],[12],[13]). Исходное определение …

Necessary and sufficient conditions are obtained for the splitting of a hereditary cotorsion
radical on the category ℳ R of right R-modules. It is shown that for injective cogenerator …

From a chronological point of view, this work is written from its end to its beginning. So let us
start at the end, which is the beginning. Background and Motivation. Quadratic and hermitian …

A Review To Some Properties of Semiperfect and Quasi- Frobenius Rings Page 1 او ا م ا ا ﺍﻠﻤﺠﻠﺪ
)1( ، ﺍﻠﻌﺪﺪ )1( ، ﻳﻮﻨﻴﻮ 2016 84 A Review To Some Properties of Semiperfect and Quasi- Frobenius …

The study of rings over which the direct sums of modules have certain properties is a well
recognized topic for research in Ring Theory and Homological Algebra. In this dissertation …

We study conditions on an ideal A of a self-injective R such that the factor ring R/A is again
self-injective, extending certain of our results for PF rings (Faith,). We also consider the same …