Mathematics and Statistics Vol. 2(7), pp. 240 - 244
DOI: 10.13189/ms.2014.020704
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Torsion Theory and its Applications in M − D Modules

Behnam Talaee ^*
Department of Mathematics, Faculty of Basic Sciences, Babol University of Technology, Babol, Iran

ABSTRACT

Let R be a ring and M an R−module. A module N ∈ [M] is called M-small if, N ≪ K for some K ∈ [M]. Torsion theory cogenerated by M−small modules is introduced and investigated in [9]. Also as a generalization of M−small modules, −M−small modules are studied in [6]. In this paper we will introduce M−delta (briefly M − D) modules and investigate the torsion theory cogenerated by such modules. We will get some equivalent conditions for when N is equal to its torsion theory submodule cogenerated by M − D modules. Especially we show that D(N;A) = 0 for all A ∈ [M] iff N = ReD[M](N). Some other important properties about this kind of modules will be obtained.

KEYWORDS
M − D Module, Torsion Theory Cogenerated by M − D Module, D−coclosed, M−coD Inclusion

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Behnam Talaee , "Torsion Theory and its Applications in M − D Modules," Mathematics and Statistics, Vol. 2, No. 7, pp. 240 - 244, 2014. DOI: 10.13189/ms.2014.020704.

(b). APA Format:
Behnam Talaee (2014). Torsion Theory and its Applications in M − D Modules. Mathematics and Statistics, 2(7), 240 - 244. DOI: 10.13189/ms.2014.020704.