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ℒ-Injective Hulls of Modules

Published online by Cambridge University Press:  17 April 2009

Lixin Mao  and
Nanqing Ding
Lixin Mao
Affiliation:
Department of Basic Courses, Nanjing Institute of Technology, Nanjing 211167, ChinaDepartment of Mathematics, Nanjing University, Nanjing 210093, China, e-mail: maolx2@hotmail.com
Nanqing Ding
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, China, e-mail: nqding@nju.edu.cn
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Let R be a ring and ℒ a class of R-modules. An R-module N is called ℒ-injective if for all L ∈ ℒ. An ℒ-injective hull of an R-module M is defined to be a homomorphism φ: M → F with F ℒ-injective such that for any monomorphism f: M → F′ with F′ ℒ-injective, there is a monomorphism g: F → F′ satisfying gφ = f. The aim of this paper is to study ℒ-injective hulls and their relations with ℒ-injective envelopes in Enochs' sense.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 1 , August 2006 , pp. 37 - 44
Copyright
Copyright © Australian Mathematical Society 2006

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