Journal ArticleDOI
On & - semisimple rings. A study of the socle of a ring
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In this article, the socle of a ring is studied in terms of semisimple rings, and it is shown that a ring socle can be constructed from a ring's socle.Abstract:
(1980). On & - semisimple rings. A study of the socle of a ring. Communications in Algebra: Vol. 8, No. 10, pp. 889-909.read more
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Rings with projective socle
W. K. Nicholson,J.F. Watters +1 more
TL;DR: The class of rings with projective left socle is shown to be closed under the formation of polynomial and power series extensions, direct prod- ucts, and matrix rings as mentioned in this paper.
Journal Article
Generalized $V$-rings and von Neumann regular rings
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.unipd.org/legal. php) of the agreement with the Rendiconti del Seminario Matematico della Università di Padova are discussed.
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Cotorsion modules and relative pure-injectivity
Lixin Mao,Nanquing Ding +1 more
TL;DR: In this article, the authors characterize rings satisfying the condition that every cotorsion right (left) module is injective with respect to a certain class of right left ideals.
References
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Book
Rings and Categories of Modules
Frank W. Anderson,Kent R. Fuller +1 more
TL;DR: In this paper, the authors provide a self-contained account of much of the theory of rings and modules, focusing on the relationship between the one-sided ideal structure a ring may possess and the behavior of its categories of modules.
Book ChapterDOI
Some properties of TTF-classes
TL;DR: In this article, it was shown that a torsion theory over a ring R on the left with a TTF-class determined by an idemotent ideal I is hereditary if and only if I is a direct s, d of R or I is flat as a right R-module respectively.
Journal ArticleDOI
Rings in which minimal left ideals are projective
TL;DR: In this paper, it was shown that a ring with finitely generated left socle and no nilpotent minimal left ideals is a ring direct sum of a semisimple artinian ring and a ring having zero socle.