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Publication Date
Sun Dec 02 2012
Journal Name
Baghdad Science Journal
Volume
9
Issue Number
4
DOI
10.21123/bsj.2012.9.4.720-727
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bsj-1418
Semi – Bounded Modules
"Commutative ring
R-module
semi-bounded modules"
Adwia Jassim Abdul-Al-Kalik
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Let R be a commutative ring with identity, and let M be a unity R-module. M is called a bounded R-module provided that there exists an element x?M such that annR(M) = annR(x). As a generalization of this concept, a concept of semi-bounded module has been introduced as follows: M is called a semi-bounded if there exists an element x?M such that . In this paper, some properties and characterizations of semi-bounded modules are given. Also, various basic results about semi-bounded modules are considered. Moreover, some relations between semi-bounded modules and other types of modules are considered.

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Pairwise Lower Separation Axioms in C ̌ech Fuzzy Soft Bi-Closure Spaces
Fuzzy soft set
fuzzy soft closure operator
closed fuzzy soft set
fuzzy soft bitopological space
pairwise 〖 T〗_0
pairwise T_1
pairwise〖 T〗_2
pairwise semi〖 T〗_2
pairwise pseudo〖 T〗_2
pairwise Uryshon 〖 T〗_2.
Mohamad Th.
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The idea of ech fuzzy soft bi-closure space ( bicsp) is a new one, and its basic features are defined and studied in [1]. In this paper, separation axioms, namely pairwise, , pairwise semi-(respectively, pairwise pseudo and pairwise Uryshon) - fs bicsp's are introduced and studied in both ech fuzzy soft bi-closure space and their induced fuzzy soft bitopological spaces. It is shown that hereditary property is satisfied for , with respect to ech fuzzy soft bi-closure space but for other mentioned types of separations axioms, hereditary property satisfies for closed subspaces of ech fuzzy soft bi-closure space.

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