A Generalization of M-Small Modules

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Talaee B.

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Journal: Journal of Sciences, Islamic Republic of Iran Year:2015 | Volume:26 | Issue:2 Page(s): 179-185

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Title

A Generalization of M-Small Modules

Author(s)

Talaee B. | Issue Writer Certificate

Keywords

small module

Rad modules

Torsion theory cogenerated by M

Rad modules

Abstract

In this paper we introduce a generalization of M-small modules and discuss about the torsion theory cogenerated by this kind of modules in category  [M]. We will use the structure of the radical of a module in  [M] and get some suitable results about this class of modules. Also the relation between injective hull in  [M] and this kind of modules will be investigated in this article. For a module N   [M] we show that N is M-Rad if and only if ) ˆ (N Rad N  ; where Nˆ is the M-injective hull of N. We will show that for a   cohereditary module M, R[M] is closed under extension. Let M be a module and N   [M], the torsion theory cogenerated by R[M] is the reject of R[M] in N, defined as ( ) = { | } [ ] is M Rad X Re N X N N R M    . In this paper we study about the property of this torsion theory. We show that = ( ) [ ] N Re N R M if and only if for every nonzero homomorphism f: N  K in  [M], Im( f )  Rad(K). Another attractive result is = ( ) [ ] N Re N R M if and only if  (N, A) = 0, for all A  [M]. For a module N   [M] we show that if ( ) K Rad N K L  for some K  L  N, then the inclusion K  L is M-coRad and also if N  R[M] , then for every submodule L of N and McoRad inclusion K  L, we have ( ) K Rad N K L  . Finally for a pseudo projective module M we show that every N   [M] with Hom(M, N) = 0 is M-Rad and if moreover M  R[M] , then R[M] ={N   [M]| Hom(M, N) = 0}.

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APA: Copy

Talaee, B.. (2015). A Generalization of M-Small Modules. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, 26(2), 179-185. SID. https://sid.ir/paper/718847/en

Vancouver: Copy

Talaee B.. A Generalization of M-Small Modules. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN[Internet]. 2015;26(2):179-185. Available from: https://sid.ir/paper/718847/en

IEEE: Copy

B. Talaee, “A Generalization of M-Small Modules,” JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, vol. 26, no. 2, pp. 179–185, 2015, [Online]. Available: https://sid.ir/paper/718847/en

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