On Objects with a Semilocal Endomorphism Rings in Finitely Accessible Additive Categories

被引：4

作者：

Berktas, Mustafa Kemal ^{[1
]}

机构：

[1] Usak Univ, Usak, Turkey

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2015年 / 18卷 / 05期

关键词：

Accessible categories; Grothendieck categories; Camps-Dicks theorem; Pure Goldie dimension; MODULES;

D O I：

10.1007/s10468-015-9545-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that if A is an object in a finitely accessible additive category A such that A has finite pure Goldie dimension and that every pure monomorphism A -> A is an isomorphism, then its endomorphism ring End(A)(A) is semilocal.

引用

页码：1389 / 1393

页数：5

共 12 条

[1]

Adamek J., 1994, LOCALLY PRESENTABLE

[2] Left cotorsion rings [J].

Asensio, PAG ;

Herzog, I .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2004, 36 :303-309

[3]

Berktas MK, 2012, JP J ALGEBR NUMBER T, V25, P113

[4] A Uniqueness Theorem in a Finitely Accessible Additive Category [J].

Berktas, Mustafa Kemal .

ALGEBRAS AND REPRESENTATION THEORY, 2014, 17 (03) :1009-1012

[5] ON SEMILOCAL RINGS [J].

CAMPS, R ;

DICKS, W .

ISRAEL JOURNAL OF MATHEMATICS, 1993, 81 (1-2) :203-211

[6] LOCALLY FINITELY PRESENTED ADDITIVE CATEGORIES [J].

CRAWLEYBOEVEY, W .

COMMUNICATIONS IN ALGEBRA, 1994, 22 (05) :1641-1674

[7]

Facchini A., 2013, MODULE THEORY ENDOMO, V167

[8] Local morphisms and modules with a semilocal endomorphism ring [J].

Facchini, Alberto ;

Herbera, Dolors .

ALGEBRAS AND REPRESENTATION THEORY, 2006, 9 (04) :403-422

[9] Modules with semi-local endomorphism ring [J].

Herbera, D ;

Shamsuddin, A .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (12) :3593-3600

[10] PURE-INJECTIVE ENVELOPES [J].

Herzog, Ivo .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2003, 2 (04) :397-402

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