Flat endofinite modules, prime ideals, and duality.

被引：1

作者：

Rump, Wolfgang ^{[1
]}

Schmider, Simon ^{[2
]}

机构：

[1] Univ Stuttgart, Inst Algebra & Number Theory, D-70550 Stuttgart, Germany

[2] Tech Univ Kaiserslautern, Dept Math, D-67663 Kaiserslautern, Germany

来源：

JOURNAL OF ALGEBRA | 2014年 / 407卷

关键词：

Generic module; Sigma-injective; Endofinite; Flat cover; Torsion theory; Character; Rank function; Local duality; Goldie prime; QF-3; ring; Quasi-Frobenius ring; ADDITIVE RANK-FUNCTIONS; INJECTIVE-MODULES; CHAIN-CONDITIONS; RINGS;

D O I：

10.1016/j.jalgebra.2014.03.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Bijective correspondences are established between endofinite injective left modules, endofinite flat right modules, finite collections of minimal noetherian prime ideals, normalized rank functions on left ideals and characters. Endofinite flat modules are identified as flat covers of modules associated to a minimal noetherian prime ideal, while endofinite flat injectives are characterized by localizations with a semiprimary QF-3 quotient ring. (c) 2014 Elsevier Inc. All rights reserved.

引用

页码：149 / 177

页数：29

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