Affiliations: [a]
Department of Mathematics, Faculty of Math. Engineering & Physics Engineering, Polytechnic University of Tirana, Tirana, ALBANIA | [b]
Department of Mathematics & Computer Science, Faculty of NaturalSciences, University of Gjirokastra, Gjirokastra, ALBANIA
Correspondence:
[*]
Corresponding author. Kostaq Hila, Department of Mathematics and Computer Science, University of Gjirokastra, ALBANIA. E-mail: [email protected].
Abstract: In this paper, applying the theory of L-fuzzy sets, we introduce the concept of an L-fuzzy ideal (L-fuzzy k-ideal) of an m-ary semigroup. Some properties of them are investigated and some structural theorems for L-fuzzy ideals (L-fuzzy k-ideals) of m-ary semigroups are proved. In this direction the concept of image and preimage of an L-fuzzy set under m-ary semigroup homomorphism are discussed. Also, the notions of normal L-fuzzy ideal (L-fuzzy k-ideal) and maximal L-fuzzy ideal (L-fuzzy k-ideal) of an m-ary semigroup are introduced and some properties of them are studied. Further, we introduce the notion of L-fuzzy congruence on an m-ary semigroup and make a study of L-fuzzy quotient m-ary semigroup using an L-fuzzy congruence, an L-fuzzy quotient m-ary semigroup induced by L-fuzzy ideals. We also investigate some properties of homomorphisms between them.
