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.

For a top semimodule over semiring with zero and nonzero identity, this paper studies the interplay between topological properties of subtractive prime spectrum algebraic semimodule. We prove that subtractively finitely generated is compact space, establish necessary sufficient conditions for to be generated. For
 multiplication commutative semiring, we radical subsemimodule coincides its ...

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.

We study the canonical weak distributive law $\delta$ of powerset monad over semimodule for a certain class semirings containing, in particular, positive semifields. For this subclass we characterise as convex closure free set. Using abstract theory laws, compose and monads via $\delta$, obtaining subsets semimodule.

1. In the first theorem of [3], Wiegandt incorrectly states that a semimodule is complete if and only if it is divisible. (See §2 for definitions.) In this paper we show (in §3) that his theorem should read: a semimodule is complete if and only if it is a divisible group. Divisible semimodules which are not necessarily groups are discussed in §4, in connection with Wiegandt's second theorem. It...

The classical lattice A ,*, whose Voronoi cells tile Euclidean n-space by permutohedra, can be given the generalized balance ternary ring structure GBT, in a natural way as a quotient ring of Z [xl. The ring GBT, can also be considered as the set of all finite sequences sO sl.. . sk, with si E GBT,/srGBT, for all i, where M is an appropriately chosen element in GBT,. The extended generalized ba...

The concept of (A,B)-invariant subspace is the fundamental concept of the geometric approach of control design. It has been extended by many authors to that of (A,B)-invariant module or semimodule, for the sake of extending the solution of various control problems to the case of systems over rings or semi rings. In this paper is discussed the use of dynamic feedback control laws for systems ove...