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http://hdl.handle.net/20.500.11889/4051
Title: | On weakly projective and weakly injective modules | Authors: | Saleh, Mohammad | Keywords: | Modules (Algebra);Commutative rings;Congruence modular varieties | Issue Date: | Jan-2004 | Abstract: | The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module M, there exists a module K ∈ σ[M] such that K ⊕ N is weakly injective in σ[M], for any N ∈ σ[M]. Similarly, if M is projective and right perfect in σ[M], then there exists a module K ∈ σ[M] such that K ⊕ N is weakly projective in σ[M], for any N ∈ σ[M]. Consequently, over a right perfect ring every module is a direct summand of a weakly projective module. For some classes M of modules in σ[M], we study when direct sums of modules from M satisfy property P in σ[M]. In particular, we get characterizations of locally countably thick modules, a generalization of locally q.f.d. modules. | URI: | http://hdl.handle.net/20.500.11889/4051 |
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On_weakly_projective_and_weakly_injective_modules.pdf | 269.88 kB | Adobe PDF | View/Open |
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