Injective dimension of generalized matrix rings

In this note, derivations on Morita rings (generalized matrix rings) are introduced and generalized derivations on rings are proved to be Morita invariant without involvement of any homology theory.

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Classical quotient rings of generalized matrix rings

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171295000391 ◽

1995 ◽

Vol 18 (2) ◽

pp. 311-316 ◽

Cited By ~ 1

Author(s):

David G. Poole ◽

Patrick N. Stewart

Keyword(s):

Associative Ring ◽

Matrix Ring ◽

Quotient Ring ◽

Matrix Rings ◽

Finite Set ◽

Generalized Matrix ◽

Quotient Rings

An associative ringRwith identity is a generalized matrix ring with idempotent setEifEis a finite set of orthogonal idempotents ofRwhose sum is1. We show that, in the presence of certain annihilator conditions, such a ring is semiprime right Goldie if and only ifeReis semiprime right Goldie for alle∈E, and we calculate the classical right quotient ring ofR.

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Ideals of generalized matrix rings

Sbornik Mathematics ◽

10.1070/sm2011v202n01abeh004135 ◽

2011 ◽

Vol 202 (1) ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Aleksandr V Budanov

Keyword(s):

Matrix Rings ◽

Generalized Matrix

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Quasi-Baer and biregular generalized matrix rings

Journal of Algebra and Its Applications ◽

10.1142/s0219498817500670 ◽

2017 ◽

Vol 16 (04) ◽

pp. 1750067 ◽

Cited By ~ 1

Author(s):

Gary F. Birkenmeier ◽

Donald D. Davis

Keyword(s):

Principal Ideal ◽

Matrix Ring ◽

Central Idempotent ◽

Matrix Rings ◽

Principal Ideals ◽

Generalized Matrix ◽

The Right

Generalized matrix rings are ubiquitous in algebra and have relevant applications to analysis. A ring is quasi-Baer (respectively, right p.q.-Baer) in case the right annihilator of any ideal (respectively, principal ideal) is generated by an idempotent. A ring is called biregular if every principal ideal is generated by a central idempotent. In this paper, we identify the ideals and principal ideals, the annihilators of ideals, and the central and semi-central idempotents of a generalized [Formula: see text] matrix ring. We characterize the generalized matrix rings that are quasi-Baer, right p.q.-Baer, prime, and biregular. We provide examples to illustrate these concepts.

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Isomorphism of generalized matrix rings

Algebra and Logic ◽

10.1007/s10469-008-9016-y ◽

2008 ◽

Vol 47 (4) ◽

pp. 258-262 ◽

Cited By ~ 26

Author(s):

P. A. Krylov

Keyword(s):

Matrix Rings ◽

Generalized Matrix

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FI-extending generalized matrix rings

Journal of Algebra and Its Applications ◽

10.1142/s0219498820500188 ◽

2019 ◽

Vol 19 (01) ◽

pp. 2050018

Author(s):

Gary F. Birkenmeier ◽

Donald D. Davis

Keyword(s):

Direct Summand ◽

Matrix Ring ◽

Sufficient Conditions ◽

Matrix Rings ◽

Generalized Matrix

Recall that a module [Formula: see text] is FI-extending if every fully invariant submodule is essential in a direct summand of [Formula: see text]. Let [Formula: see text] be a generalized matrix ring, where [Formula: see text] and [Formula: see text] are rings and [Formula: see text] and [Formula: see text] are bimodules. In this paper, we investigate necessary and/or sufficient conditions on [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text] to be FI-extending.

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