Rings which are Baer or quasi-Baer modulo a radical

被引：0

作者：

Ryan, C. Edward ^{[1
]}

机构：

[1] San Diego State Univ Imperial Valley Campus, Dept Math, Calexico, CA 92231 USA

来源：

COMMUNICATIONS IN ALGEBRA | 2021年 / 49卷 / 10期

关键词：

Baer ring; idempotent; Morita invariant; quasi-Baer ring; radical;

D O I：

10.1080/00927872.2021.1924185

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Baer and quasi-Baer rings are important classes of algebraic objects, and their properties have roots in analysis. In this paper, we investigate rings R such that R/rho(R) is Baer or quasi-Baer, where rho(R) is either the Jacobson radical or the prime radical of R. Preliminary characterizations and results are obtained; in particular, we show that the property of R/P(R) being quasi-Baer is a Morita invariant.

引用

页码：4557 / 4564

页数：8

共 14 条

[1]

[Anonymous], 2013, EXTENSIONS RINGS MOD, DOI DOI 10.1007/978-0-387-92716-9

[2] THE FACTOR RING OF A QUASI-BAER RING BY ITS PRIME RADICAL [J].

Birkenmeier, Gary F. ;

Kim, Jin Yong ;

Park, Jae Keol .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2011, 10 (01) :157-165

[3] Hulls of semiprime rings with applications to C*-algebras [J].

Birkenmeier, Gary F. ;

Park, Jae Keol ;

Rizvi, S. Tariq .

JOURNAL OF ALGEBRA, 2009, 322 (02) :327-352

[4] Triangular matrix representations [J].

Birkenmeier, GF ;

Heatherly, HE ;

Kim, JY ;

Park, JK .

JOURNAL OF ALGEBRA, 2000, 230 (02) :558-595

[5] A GENERALIZATION OF FPF RINGS [J].

BIRKENMEIER, GF .

COMMUNICATIONS IN ALGEBRA, 1989, 17 (04) :855-884

[6] Triangular matrix representations of ring extensions [J].

Birkenmeier, GF ;

Park, JK .

JOURNAL OF ALGEBRA, 2003, 265 (02) :457-477

[7] IDEMPOTENTS AND COMPLETELY SEMIPRIME IDEALS [J].

BIRKENMEIER, GF .

COMMUNICATIONS IN ALGEBRA, 1983, 11 (06) :567-580

[8] TWISTED MATRIX UNITS SEMIGROUP ALGEBRAS [J].

CLARK, WE .

DUKE MATHEMATICAL JOURNAL, 1967, 34 (03) :417-&

[9]

Jacobson N., 1956, STRUCTURE RINGS AM M, V37

[10]

Kaplansky I., 1968, RINGS OPERATORS

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