A non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.
Let be a ring with identity. Recall that a submodule of a left -module is called strongly essential if for any nonzero subset of , there is such that , i.e., . This paper introduces a class of submodules called se-closed, where a submodule of is called se-closed if it has no proper strongly essential extensions inside . We show by an example that the intersection of two se-closed submodules may not be se-closed. We say that a module is have the se-Closed Intersection Property, briefly se-CIP, if the intersection of every two se-closed submodules of is again se-closed in . Several characterizations are introduced and studied for each of these concepts. We prove for submodules and of that a module has the
... Show MoreIn a previous work, Ali and Ghawi studied closed Rickart modules. The main purpose of this paper is to define and study the properties of y-closed Rickart modules .We prove that, Let and be two -modules such that is singular. Then is -y-closed Rickart module if and only if Also, we study the direct sum of y-closed Rickart modules.
The purpose of this paper is to extend some results concerning generalized derivations to generalized semiderivations of 3-prime near rings.
Let R be a commutative ring with identity, and let M be a unitary (left) R- modul e. The ideal annRM = {r E R;rm = 0 V mE M} plays a central
role in our work. In fact, we shall be concemed with the case where annR1i1 = annR(x) for some x EM such modules will be called bounded modules.[t htrns out that there are many classes of modules properly contained in the class of bounded modules such as cyclic modules, torsion -G·ee modulcs,faithful multiplicat
... Show MoreIn this paper we study the concepts of copure submodules and coregular
modules. Many results related with these concepts are obtained.
In this paper, we introduce the concept of s.p-semisimple module. Let S be a semiradical property, we say that a module M is s.p - semisimple if for every submodule N of M, there exists a direct summand K of M such that K ≤ N and N / K has S. we prove that a module M is s.p - semisimple module if and only if for every submodule A of M, there exists a direct summand B of M such that A = B + C and C has S. Also, we prove that for a module M is s.p - semisimple if and only if for every submodule A of M, there exists an idempotent e ∊ End(M) such that e(M) ≤ A and (1- e)(A) has S.
In this paper, we investigate prime near – rings with two sided α-n-derivations
satisfying certain differential identities. Consequently, some well-known results
have been generalized. Moreover, an example proving the necessity of the primness
hypothesis is given.
Polymeric hollow fiber membrane is produced by a physical process called wet or dry/wet phase inversion; a technique includes many steps and depends on different factors (starting from selecting materials, end with post-treatment of hollow fiber membrane locally manufactured). This review highlights the most significant factors that affect and control the characterization and structure of ultrafiltration hollow fiber membranes used in different applications.
Three different types of polymers (polysulfone PSF, polyethersulfone PES or polyvinyl chloride PVC) were considered to study morphology change and structure of hollow fiber membranes in this review. These hollow fiber membranes were manufactured with different pro
... Show MoreLet be a commutative ring with 1 and be a left unitary . In this paper, the generalizations for the notions of compressible module and retractable module are given.
An is termed to be semi-essentially compressible if can be embedded in every of a non-zero semi-essential submodules. An is termed a semi-essentially retractable module, if for every non-zero semi-essentially submodule of an . Some of their advantages characterizations and examples are given. We also study the relation between these classes and some other classes of modules.
Let be a commutative ring with 1 and be left unitary . In this paper we introduced and studied concept of semi-small compressible module (a is said to be semi-small compressible module if can be embedded in every nonzero semi-small submodule of . Equivalently, is semi-small compressible module if there exists a monomorphism , , is said to be semi-small retractable module if , for every non-zero semi-small sub module in . Equivalently, is semi-small retractable if there exists a homomorphism whenever . In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible and retractable respectively and give some of their adv
... Show More