Throughout this paper we introduce the concept of quasi closed submodules which is weaker than the concept of closed submodules. By using this concept we define the class of fully extending modules, where an R-module M is called fully extending if every quasi closed submodule of M is a direct summand.This class of modules is stronger than the class of extending modules. Many results about this concept are given, also many relationships with other related concepts are introduced.
A submoduleA of amodule M is said to be strongly pure , if for each finite subset {ai} in A , (equivalently, for each a ?A) there exists ahomomorphism f : M ?A such that f(ai) = ai, ?i(f(a)=a).A module M is said to be strongly F–regular if each submodule of M is strongly pure .The main purpose of this paper is to develop the properties of strongly F–regular modules and study modules with the property that the intersection of any two strongly pure submodules is strongly pure .
Six isolates of A. pullulans were collected from many sources including Hibiscus sabdariffa (Roselle), old Roofs of houses and bathroom surface that referred as Ap ros1, Ap or2, 3, 4 and Ap bs5, 6 respectively, all these isolates were identified based on morphological characteristics and nutritional physiology profiles, all were able to utilize various carbon and nitrogen sources such as glucose, xylose, sucrose, maltose, ammonium sulfate, ammonium nitrate and ammonium chloride, also they showed positive test for starch and amylase, while α-cellulose, ethanol, and methanol were could not be ass
... Show MoreThis paper presents a fully computerized method to backup the router configuration file. The method consists of a friendly graphical interface programmed by Java programming language.
The proposed method is compared with the two existing methods, namely: TFTP server method and Copy/Paste method. The comparison reveals that the proposed method has many advantages over the existing ones. The proposed method has been implemented on Cisco routers (series 2500, 2600 and 2800).
Let Q be a left Module over a ring with identity ℝ. In this paper, we introduced the concept of T-small Quasi-Dedekind Modules as follows, An R-module Q is T-small quasi-Dedekind Module if,
Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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Let R be a commutative ring with identity, and W be a unital (left) R-module. In this paper we introduce and study the concept of a quasi-small prime modules as generalization of small prime modules.