Journal of Hyperstructures
Volume:9 Issue: 2, Summer and Autumn 2020

As a generalization of the concepts of a fuzzy prime ideal and a prime fuzzy ideal, the concepts of a fuzzy 2-absorbing ideal and a 2-absorbing fuzzy ideal of a lattice are introduced. Some results on such fuzzy ideals are proved. It is shown that the radical of a fuzzy ideal of L is a 2-absorbing fuzzy ideal if and only if it is a 2-absorbing primary fuzzy ideal of L. We also introduce and study these concepts in a product of lattices.

In this paper pseudo symmetric Γ-hyperideal in Γsemihypergroups is introduced and characterized. It is proved that the class of pseudo symmetric Γ-semihypergroups contains left (right) duo Γ-semihypergroups, quasi commutative Γ-semihypergroups with unity, left (right) pseudo commutative Γ-semihypergroups and idempotent Γ-semihypergroups. The notions of completely prime Γhyperideal, semiprime Γ-hyperideal, partially semiprime Γ- hyperideal are also defined and completely prime Γ-hyperideal of a Γsemihypergroup has been characterized in terms of prime Γ- hyperideal and pseudo symmetric Γ-hyperideal. The characterization of completely semiprime Γ-hyperideals of Γ-semihypergroups is presented. In Γ-semihypergroup n-semiprime Γ-hyperideal and npartially semiprime Γ-hyperideal are introduced as a generalization of semiprime Γ-hyperideal and partially semiprime Γ-hyperideal of Γ-semihypergroup respectively. The notion of semi-extension of Γhyperideal in Γ-semihypergroup has also been defined. Some related results are proved along with establishing the relationship between n-semiprime Γ-hyperideals and semi-extension of Γ-hyperideal in commutative Γ-semihypergroups.

In this paper, we introduce the concepts of a fuzzy essential-small submodule and a fuzzy small-essential submodule of a module. We investigate various properties of such fuzzy submodules. It is also shown that the Jacobson L-radical is the sum of all essential-small L-submodules of a module. We also prove that the L-socle is the intersection of all small-essential L-submodules of a module.

In this paper, we introduce the notion of a fuzzy αmodular pair in a fuzzy α-lattice and obtain some results.

Hyperstructure theory, initiated by Marty, is a generalization theory of classical algebraic structures, while soft set theory is a powerful mathematical approach for modeling uncertainties and imprecision. In this study, it is aimed to introduce the concept of soft topological hypergroups by presenting a soft approachto the concept of topological hypergroups, one of the topological algebraic hyperstructures. Also, by defining the concept of a soft topological transposition hypergroup, several special types of soft topological subhypergroups are presented, and then the relationships between these concepts are investigated. Later on, by constructing the category CSTH of soft topological hypergroups with soft topological homomorphisms, some related characterizations are established.

As an extension of the concept of a fuzzy subring and a fuzzy ideal, a new kind of a fuzzy subring and a fuzzy ideal called an (a, b)-fuzzy subring and an (a, b)-fuzzy ideal of a ring is defined and their properties are studied. We also investigate the preimage of an (a, b)-fuzzy subring and an (a, b)-fuzzy ideal under a ring homomorphism. Also, (a, b)-level fuzzy subrings (fuzzy ideals) are studied. A necessary and sufficient condition for two (a, b)-level fuzzy subrings (fuzzy ideals) to be equal is proved. We show that the set of cosets of an (a, b)-fuzzy ideal forms a ring.

In this paper we study growth properties of generalist iterated entire functions.