The Category of Modules on an n-Trivial Extension:the Basic Properties

• 作者: Dirar Benkhadra Driss Bennis J.R.García Rozas
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 607-620
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386720000504

摘要

In this paper we investigate a categorical aspect of n-trivial extension of a ring by a family of modules.Namely,we introduce the right (resp.,left) n-trivial extension of a category by a family of endofunctors.Among other results,projective,injective and fiat objects of this category are characterized,and two applications are presented at the end of this paper.We characterize when an n-trivial extension ring is k-perfect and establish a result on the self-injective dimension of an n-trivial extension ring.