الخلاصة

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 .