Shukur Neamah Mobred Al-Aeashi

Abstract: A new generalizations of coretractable modules are introduced where a module M is called t-essentially (weakly t-essentially) coretractable if for all proper submodule K of M, there exists f∈End(M), f(K)=0 and Imf≤tes M (Im f +K≤tes M). Some basic properties are studied and many relationships between these classes and other related one are presented. Keywords: Coretractable module; essentially coretractable module; t-essentially coretractable module; weakly t-essentially coretractable module; weakly essentially coretractable module.

In this paper, we define a new notion namely compressible relative to a submodule also, a new generalizations of compressible modules relative to a submodule are introduced where a module ℳ is called compressible module relative to a submodule N of M if for all non-zero submodule K of ℳ such that contains N, there exists a monomorphism f∈Hom(ℳ, K). Some basic properties are studied and many relationships between these classes and other related concepts are presented and studied. Keywords: Compressible module relative to a submodule, Retractable module relative to a submodule.

In this paper, we introduce the notion of fully dual closed stable module as a generalization of fully dual stable. Some basic properties of this notion are given. Also the related modules with this notion are introduced and studied. Key Words: fully stable module; fully closed stable module; fully dual stable module; fully dual closed stable module.

A new generalizations of retractable modules relative to a submodule are introduced where a module ℳ is called retractable module relative to a submodule N of M if for all non-zero submodule K of ℳ such that contains N, there exists a non-zero homomorphism f∈Hom(ℳ, K). Some basic properties are studied and many relationships between these classes and other related concepts are presented and studied. Keywords: Retractable module relative to a submodule, coretractable module relative to a submodule.

Abstract: In this paper, we introduce and study type of modules namely (t-essentially quasi-Dedekind modules) which is generalization of quasi-Dedekind modules and essentially quasi-Dedekind module. Also, we introduce the class of t-essentially prime modules which contains the class of t-essentially quasi-Dedekind modules.

In this paper, we introduce two new notions related with coretrectable modules which are called essentially coretrectable and weakly essentially coretrectable modules. Some basic properties of these classes are investigated and some relationships between these modules and other related concepts are given.

In this paper, as generalization of second modules we introduce type of modules namely (essentially second modules). A comprehensive study of this class of modules is given, also many results concerned with this type and other related modules presented.

Conference of Ibn-Al-Haitham College

مؤتمر كلية العلوم / جامعة النهرين الدولي

Abstract In this paper, we give many new relationships between coretractable modules and other related concept. Moreover, we study many generalizations of coretractable modules and give many connections between them and coretractable modules. Indexing terms/Keywords: coretractable modules, Rickart modules, epi-coretrractable modules, mono-coretractable modules, fi-coretractable modules and Endocoprime modules.

Throughout this paper, all rings have identities and all modules are unitary right modules. Let R be a ring and M an R-module. A module M is called coretractable if for each proper submodule N of M, there exists a nonzero homomorphism f from M/N into M. Our concern in this paper is to develop basic properties of coretractable modules and to look for any relations between coretractable modules and other classes of modules. SOME RESULTS ABOUT CORETRACTABLE MODULES. Available from: https://www.researchgate.net/publication/319256561_SOME_RESULTS_ABOUT_CORETRACTABLE_MODULES [accessed Aug 27, 2017].

Let R be a ring with identity and M be an R-module with unity . In this paper we introduce the notion of strongly coretractable modules . Where M is called strongly coretractable module if for each proper submodule N of M , there exists a nonzero R-homomorphism f:M/N→M such that Imf+N=M . Some basic properties of this class of modules are investigated and some relationships between these modules and other related concepts are introduced . Keywords and phrases : coretractable modules , strongly coretractable modules , epi-coretractable and coquasi-Dedekind module .

Let R be a ring with identity and M be an R-module with unitary . In this paper we introduce the notion of Y-coretractable module . Some basic properties of this class of modules are investigated and some relationships between these modules and other related concepts are introduced . Keywords and phrases: coretractable module , Y-coretractable module , C-coretractable module

Abstract In this paper , some results about the concept of completely coretractable ring are studied and also another results about the coretractable module are recalled and investigated. Indexing terms/Keywords : coretractable module , completely coretractable ring. SUBJECT CLASSIFICATION 16D10; 16D40.

ABSTRACT— In this paper, we introduce the notion of P-coretractable module . Some basic properties of this class of modules are investigated and some relationships between these modules and other related concepts are introduced . Also , we give the notion of strongly P-coretractable and study it comparison with P-coretractable , moreover the mono-P-coretractable concept are introduced and studied . Keywords— :(strongly) coretractable modules, (strongly) P-coretractable , mono-coretractable , mono-P-coretractable , purely-Rickart .

Abstract Let R be a ring with identity and M be an R-module with unite . The module M is called strongly coretractable module if for each proper submodule N of M , there exists a nonzero R-homomorphism f:M/N→M such that Imf+N=M . In this paper we investigate some relationships between strongly coretractable module and other related concepts .

In this paper, we introduce the notion of a completely semi essential fuzzy submodule which connect between the concept of essential fuzzy submodule and semi essential fuzzy submodule and we give some properties of this concept. COMPLETELY SEMI ESSENTIAL FUZZY SUBMODULE Shukur Neamah Al-aeashi DEPARTMENT OF URBAN PLANNING ,COLLEGE OF PHYSICAL PLANNING, UNIVERSITY OF KUFA E-mail: [email protected] Abstract In this paper, we introduce the notion of a completely semi essential fuzzy submodule which connect between the concept of essential fuzzy submodule and semi essential fuzzy submodule and we give some properties of this concept. 1 Introduction The concept of fuzzy sets was introduced by Zadeh in 1965 [9]. It was first applied in the theory of groups by Rosenfeld in 1971 [8] . The concept of fuzzy module was introduced by Negoita and Relescu in 1975 [4]. Since then several authors have studied fuzzy modules. The concept of essential fuzzy submodule was introduced by Hadi 2000[2] . In this paper Let R be a commutative ring with unity and let M be unitary R-module . we list some known properties of essential submodules and we present some known characterizations of essential submodules which are relative to our work. we introduce a completely semi essential submodule concept. Also we generalize some known properties of essential fuzzy submodules to completely semi essential fuzzy submodules. Key words essential (fuzzy) submodule, semi essential (fuzzy) submodule, completely semi essential (fuzzy) submodule .

In this paper, we introduce the concept of 2-semi essential submodule in Ordinary and fuzzy senses also we give some related properties of this concept study the relationships between this concepts and the concepts of semi essential and essential submodule in ordinary and fuzzy senses. Introduction The concept of fuzzy sets was introduced by Zadeh in 1965 [11]. It was first applied to the theory of groups by Rosenfeld in 1971 [10] . Since then, many authors introduced fuzzy subring and fuzzy ideals[8] .The concept of fuzzy module was introduced by Negoita and Relescu in 1975 [1]. Since then several authors have studied fuzzy modules. The concept of essential fuzzy submodule was introduced by Hadi in 2000[9], Al-daban introduced and studied the concept of semi essential submodule in 2005 [2] . Maysoun fuzzified this concept and studied some its properties in 2009 .in this work , we introduce the concept of 2-semi essential submodule over a left commutative ring with unity and a unitary R-module .

In this paper, we study the concept of uniform fuzzy module and essential fuzzy submodule. Also we give some of characteristics about

In this paper, we study the concept of uniform fuzzy module and essential fuzzy submodule. Also we give some of characteristics about

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the third Examination