Triangular matrix representations of ring extensions

被引：104

作者：

Birkenmeier, GF ^{[1
]}

Park, JK

机构：

[1] Univ SW Louisiana, Dept Math, Lafayette, LA 70504 USA

[2] Busan Natl Univ, Dept Math, Pusan 609735, South Korea

来源：

JOURNAL OF ALGEBRA | 2003年 / 265卷 / 02期

关键词：

generalized triangular matrix representation; ring extension; centralizing extension; normalizing extension; quasinormalizing extension; piecewise domain; piecewise prime ring; principally quasi-Baer ring; quasi-Baer ring; semicentral idempotent; triangulating dimension; triangulating idempotent; u.p.-monoid ring;

D O I：

10.1016/S0021-8693(03)00155-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate the class of piecewise prime, PWP, rings which properly includes all piecewise domains (hence all right hereditary rings which are semiprimary or right Noetherian). For a PWP ring we determine a large class of ring extensions which have a generalized triangular matrix representation for which the diagonal rings are prime. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：457 / 477

页数：21

共 33 条

[1]

Armendariz E.P., 1974, J AUSTR MATH SOC, V18, P470

[2]

ARMENDARIZ EP, ORE EXTENSIONS NEUMA

[3] Polycyclic group rings whose principal ideals are projective [J].

Behn, A .

JOURNAL OF ALGEBRA, 2000, 232 (02) :697-707

[4]

Birkenmeier G.F., 2000, Kyungpook Math. J, V40, P247

[5] Triangular matrix representations [J].

Birkenmeier, GF ;

Heatherly, HE ;

Kim, JY ;

Park, JK .

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

[6] Quasi-Baer ring extensions and biregrular rings [J].

Birkenmeier, GF ;

Kim, JY ;

Park, JK .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2000, 61 (01) :39-52

[7] BAER RINGS AND QUASICONTINUOUS RINGS HAVE A MDSN [J].

BIRKENMEIER, GF .

PACIFIC JOURNAL OF MATHEMATICS, 1981, 97 (02) :283-292

[8] DECOMPOSITIONS OF BAER-LIKE RINGS [J].

BIRKENMEIER, GF .

ACTA MATHEMATICA HUNGARICA, 1992, 59 (3-4) :319-326

[9] A sheaf representation of quasi-Baer rings [J].

Birkenmeier, GF ;

Kim, JY ;

Park, JK .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2000, 146 (03) :209-223

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

BIRKENMEIER, GF .

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

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