¡v in this paper we consider a strongly regular relation ƒá on hypermodules so that the quotient is amodule (with abelian group) over a fundamental commutative ring. also, we state necessary and sufficientconditions so that the relation ƒá is transitive, and finally we prove that ƒá is transitive on hypermodules.

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...

We consider so-called Fatou-type properties of rational languages and relations. For example, if the rational expression E(X1; : : : ; Xn) over arbitrary languages X1; : : : ;Xn represents a rational language, then each language Xi can be replaced by a rational language Yi such that E(X1; : : : ;Xn) = E(Y1; : : : ; Yn) holds and moreover Xi Yi for i = 1; : : : ; n. Some similar results for rati...

Bonin et al. (1993) recalled an open problem related to the recurrence relation verified by NSW numbers. The recurrence relation is the following: fn+l = 6f~ f~l , with jq = 1 and j~ = 7, and no combinatorial interpretation seems to be known. In this note, we define a regular language .~ whose number of words having length n is equal to f~+l. Then, by using .La we give a direct combinatorial pr...

In this paper, by considering the notion of $Sigma$-hyperalgebras for an arbitrary signature $Sigma$, we study the notions of regular and strongly regular relations on a $Sigma$-hyperalgebra, $mathfrak{A}$. We show that each regular relation which contains a strongly regular relation is a strongly regular relation. Then we concentrate on the connection between the fundamental relation of $mathf...

The concept of algebraic hyperstructures introduced by Marty as a generalization of ordinary algebraic structures. In an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper‌rings and a generalizat...

the aim of this paper is to initiate and investigate new soft sets over semihypergroups, named special soft sets and transitive soft sets and denoted by $s_{h}$ and  $t_{h},$ respectively. it is shown that $t_{h}=s_{h}$ if and only if $beta=beta^{*}.$ we also introduce the derived semihypergroup from a special soft set and study some properties of this class of semihypergroups.

In this paper four regular relations, R, L∗, M∗ and Q∗ in a transformation group (X, T ) are defined and some of their properties are studied.

We provide an exact estimate on the maximal subword complexity for quasiperiodic infinite words. To this end we give a representation of the set of finite and of infinite words having a certain quasiperiod q via a finite language derived from q. It is shown that this language is a suffix code having a bounded delay of decipherability. Our estimate of the subword complexity uses this property, e...