TRIANGULAR MATRIX REPRESENTATIONS OF SEMIPRIMARY RINGS-Reference-Cited by-同舟云学术

TRIANGULAR MATRIX REPRESENTATIONS OF SEMIPRIMARY RINGS

Published:2002-06 Issue:02 Volume:01 Page:123-131
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

BIRKENMEIER GARY F.¹,KIM JIN YONG²,PARK JAE KEOL³

Affiliation:

1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010, U.S.A.

2. Institute of Natural Sciences, Kyung Hee University, Suwon 449-701, South Korea

3. Department of Mathematics, Busan National University, Busan 609-735, South Korea

Abstract

In this paper we characterize internally a TSA ring (i.e. a generalized triangular matrix ring with simple Artinian rings on the diagonal) in terms of its prime ideals. Also we show that the class of semiprimary quasi-Baer rings is a proper subclass of the class of TSA rings. Moreover, we generalize results of Harada, Small, and Teply on semiprimary rings. Finally we prove that under certain cardinality conditions a semiprimary quasi-Baer ring becomes semisimple Artinian.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498802000057

Reference15 articles.

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2. Idempotents and completely semiprime ideals

3. Decompositions of Baer-like rings

4. Triangular Matrix Representations

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