Covering classes and uniserial modules

JOURNAL OF ALGEBRA

卷:570

Article

Facchini, Alberto¹  Nazemian, Zahra²  Prihoda, Pavel³ 

[1] Univ Padua, Dipartimento Matemat, I-35121 Padua, Italy

[2] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

[3] Charles Univ Prague, Fac Math & Phys, Dept Algebra, Sokolovska 83, Prague 18675 8, Czech Republic

关键词: Weakly generating set;    Uniserial module;    Covering class;   

DOI  :  10.1016/j.jalgebra.2020.11.011

来源: Elsevier

【 摘 要 】

We apply minimal weakly generating sets to study the existence of Add(U-R)-covers for a uniserial module U-R. If U-R is a uniserial right module over a ring R, then S := End(U-R) has at most two maximal (right, left, two-sided) ideals: one is the set I of all endomorphisms that are not injective, and the other is the set K of all endomorphisms of U-R that are not surjective. We prove that if U-R is either finitely generated, or artinian, or I subset of K, then the class Add(U-R) is covering if and only if it is closed under direct limit. Moreover, we study endomorphism rings of artinian uniserial modules giving several examples. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free