STRONG EXCHANGE RINGS

被引：1

作者：

Cortes-Izurdiaga, Manuel ^{[1
]}

Asensio, Pedro A. Guil ^{[2
]}

机构：

[1] Univ Malaga, Dept Matemat Aplicada, Malaga 29071, Spain

[2] Univ Murcia, Dept Matemat, Murcia 30100, Spain

来源：

PUBLICACIONS MATEMATIQUES | 2023年 / 67卷 / 02期

关键词：

exchange rings; von Neumann regular rings; semiregular rings; (pure-)injective rings; coprime pair; STABLE RANGE; DECOMPOSITIONS; MODULES;

D O I：

10.5565/PUBLMAT6722303

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Two elements a, b in a ring R form a right coprime pair, written (a, b), if aR + bR = R. Right coprime pairs have shown to be quite useful in the study of left cotorsion or exchange rings. In this paper, we define the class of right strong exchange rings in terms of descending chains of them. We show that they are semiregular and that this class of rings contains left injective, left pure-injective, left cotorsion, local, and left continuous rings. This allows us to give a unified study of all these classes of rings in terms of the behaviour of descending chains of right coprime pairs.

引用

页码：541 / 567

页数：27

共 21 条

[1] Anderson F.W., 1992, Graduate Texts in Mathematics, V13, DOI 10.1007/978-1-4612-4418-9
[2] Left cotorsion rings
Asensio, PAG
Herzog, I
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2004, 36 : 303 - 309
[3] Continuous modules are clean
Camillo, V. P.
Khurana, D.
Lam, T. Y.
Nicholson, W. K.
Zhou, Y.
[J]. JOURNAL OF ALGEBRA, 2006, 304 (01) : 94 - 111
[4] EXCHANGE RINGS, UNITS AND IDEMPOTENTS
CAMILLO, VP
YU, HP
[J]. COMMUNICATIONS IN ALGEBRA, 1994, 22 (12) : 4737 - 4749
[5] REFINEMENTS FOR INFINITE DIRECT DECOMPOSITIONS OF ALGEBRAIC SYSTEMS
CRAWLEY, P
JONSSON, B
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1964, 14 (03) : 797 - &
[6] Goodearl K. R., 1991, Von neumann regular rings
[7] ALGEBRAS OVER ZERO-DIMENSIONAL RINGS
GOODEARL, KR
WARFIELD, RB
[J]. MATHEMATISCHE ANNALEN, 1976, 223 (02) : 157 - 168
[8] GOODEARL KR, 1976, RING THEORY NONSINGU
[9] Jensen Christian U., 1989, MODEL THEORETIC ALGE, V2
[10] EXCHANGE ELEMENTS IN RINGS, AND THE EQUATION XA - BX = I
Khurana, Dinesh
Lam, T. Y.
Nielsen, Pace P.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (01) : 495 - 516

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