scholarly journals Injective dimension of generalized matrix rings

1984 ◽  
Vol 8 (2) ◽  
pp. 339-352
Author(s):  
Kazunori Sakano
Keyword(s):  
Injective Dimension ◽  
Matrix Rings ◽  
Generalized Matrix

DERIVATIONS ON MORITA RINGS AND GENERALIZED DERIVATIONS

2011 ◽  
Vol 10 (02) ◽  
pp. 191-200 ◽  
Author(s):  
S. AL-NOFAYEE ◽  
S. K. NAUMAN
Keyword(s):  
Homology Theory ◽  
Generalized Derivations ◽  
Matrix Rings ◽  
Morita Invariant ◽  
Generalized Matrix

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.

scholarly journals Classical quotient rings of generalized matrix rings

1995 ◽  
Vol 18 (2) ◽  
pp. 311-316 ◽  
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.

Ideals of generalized matrix rings

2011 ◽  
Vol 202 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Aleksandr V Budanov
Keyword(s):  
Matrix Rings ◽  
Generalized Matrix

Quasi-Baer and biregular generalized matrix rings

2017 ◽  
Vol 16 (04) ◽  
pp. 1750067 ◽  
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.

Isomorphism of generalized matrix rings

2008 ◽  
Vol 47 (4) ◽  
pp. 258-262 ◽  
Author(s):  
P. A. Krylov
Keyword(s):  
Matrix Rings ◽  
Generalized Matrix

FI-extending generalized matrix rings

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.

Quasipolar Property of Generalized Matrix Rings

2014 ◽  
Vol 42 (9) ◽  
pp. 3883-3894 ◽  
Author(s):  
Qinghe Huang ◽  
Gaohua Tang ◽  
Yiqiang Zhou
Keyword(s):  
Matrix Rings ◽  
Generalized Matrix

Trivial generalized matrix rings

2016 ◽  
pp. 138-151
Author(s):  
G. F. Birkenmeier ◽  
B. J. Heider
Keyword(s):  
Matrix Rings ◽  
Generalized Matrix
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