الخلاصة

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 .