in this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. we prove that if $n$ is a weakly prime subtractive ternary subsemimodule of a ternary $r$-semimodule $m$, then either $n$ is a prime ternary subsemimodule or $(n : m)(n : m)n = 0$. if $n$ is a $q$-...

In this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. We prove that if $N$ is a weakly prime subtractive ternary subsemimodule of a ternary $R$-semimodule $M$, then either $N$ is a prime ternary subsemimodule or $(N : M)(N : M)N = 0$. If $N$ is a $Q$-...

Modes are idempotent and entropic algebras. Although it had been established many years ago that groupoid modes embed as subreducts of semimodules over commutative semirings, the general embeddability question remained open until M. Stronkowski and D. Stanovský’s recent constructions of isolated examples of modes without such an embedding. The current paper now presents a broad class of modes t...

We define and study basic properties of ∗-continuous Kleene ω-algebras that involve a ∗-continuous Kleene algebra with a ∗-continuous action on a semimodule and an infinite product operation that is also ∗-continuous. We show that ∗-continuous Kleene ω-algebras give rise to iteration semiring-semimodule pairs. We show how our work can be applied to solve certain energy problems for hybrid systems.

A modernization of signature scheme published in (Sakalauskas, 2004) is presented. This scheme differs from the prototype by its structure and uses a more general algebraic systems. It has a higher security and shorter key length and is also more computationally effective. The introduced new algebraic structures, semiring and semimodule, are mutually compatible algebraic systems. The semiring i...

A category with biproducts is enriched over (commutative) additive monoids. A category with tensor products is enriched over scalar multiplication actions. A symmetric monoidal category with biproducts is enriched over semimodules. We show that these extensions of enrichment (e.g. from hom-sets to homsemimodules) are functorial, and use them to make precise the intuition that “compact objects a...

A New generalization of injective semimodule has been presented in this working paper. An Ȑ-semimodule Ӎ is called almost self-injective, if Ӎ-injective semimodule. Some properties notion have presented. The relationship concept to some concepts also clarified as End (Ȑ) indecomposable self-injective semimodules, Rad related notions it studied.

Let be a commutative semiring. A semimodule over semiring is fully prime if each proper subsemimodule of prime. This research aims to investigate the relationship between direct sum subsemimodules and , semimodule.