We introduce max-plus analogues of basic Euclidian geometry notions: scalar product is replaced by a scalar division, and the associated distance is essentially Hilbert’s projective distance. We introduce an orthogonal projection and prove a Hahn-Banach type theorem: a point can be separated from a semimodule by a hyperplane orthogonal to the direction of projection. We use these results to sep...

An algebra is entropic if its basic operations are homomorphisms. The paper is focused on representations of such algebras. We prove the following theorem: An entropic algebra without constant basic operations which satisfies so called Szendrei identities and such that all its basic operations of arity at least two are surjective is a subreduct of a semimodule over a commutative semiring. Our t...

In this paper, we introduce and study the concepts of prime left, semiprime left and irreducible left hyperideals in ternary semihyper- groups and investigate some basic properties of them. We introduce the concepts of hyper lter and hypersemilattice congruence of ternary semi- hypergroups. We give some characterizations of hyper lters in ternary semihypergroups. Some relationships between hype...

A new theoretical model based on the local composition concept (TNRF-mNRTL model) was proposed to express the short-range contribution of the excess Gibbs energy for the solutions containing polymer and electrolyte. This contribution of interaction along with the long-range contribution of interaction (Pitzer-Debye-Hückel equation), configurational entropy of mixing (Flory-Huggins relation)...

In a ternary semihyperring, addition is a hyperoperation and multiplicationis a ternary operation. Indeed, the notion of ternary semihyperringsis a generalization of semirings. Our main purpose of this paper is to introducethe notions of fuzzy hyperideal and fuzzy bi-hyperideal in ternary semihyperrings.We give some characterizations of fuzzy hyperideals and investigateseveral kinds of them.

To my dearest friend Najla Ali We introduce and investigate flat semimodules and k-flat semimodules. We hope these concepts will have the same importance in semimodule theory as in the theory of rings and modules. 1. Introduction. We introduce the notion of flat and k-flat. In Section 2, we study the structure ensuing from these notions. Proposition 2.4 asserts that V is flat if and only if (V ...

In [16], by using an MV-semiring and MV-algebra, we introduced the new definition of MV-semimodule studied some their basic properties. this paper, study present definitions primary ideals MV-semirings, decomposition in A-ideals MV -semimodules, MV-semimodules. Then conditions that A-ideal can have a reduced decomposition.