In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups . Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper.

This paper investigates the S -transform on the space of tempered Boehmians. Inversion and properties are also discussed.

We establish a bridge between homotopy groups of spheres and commutator calculus in groups, solve this manner the “dimension problem” by providing converse to Sjogren's theorem: every abelian group bounded exponent can be embedded dimension quotient group. This is proven embedding for arbitrary s , d $s,d$ torsion π ( S ) $\pi _s(S^d)$ into quotient, via result Wu. In particular, invalidates so...

This short, expository note proves existence of the maximal quotient of a variety by free rational curves. 1. Definition of a maximal free rational quotient Definition 1.1. Let V be a Deligne-Mumford stack over a field k, and denote the smooth locus by V sm ⊂ V . A 1-morphism f : Pk → V sm is a free rational curve to V if fTV is generated by global sections and has positive degree. Let S be an ...

Abstract A natural operation on numerical semigroups is taking a quotient by positive integer. If $\mathcal {S}$ of semigroup with k generators, we call -quotient. We give necessary condition for given to be -quotient and present, each $k \ge 3$ , the first known family that cannot written as also examine probability randomly selected generators

For an arbitrary ring R, the largest strong left quotient ring Ql (R) of R and the strong left localization radical lR are introduced and their properties are studied in detail. In particular, it is proved that Ql (Q s l (R)) ≃ Q s l (R), l s R/ls R = 0 and a criterion is given for the ring Ql (R) to be a semisimple ring. There is a canonical homomorphism from the classical left quotient ring Q...

An ordered semigroup is a structure S = 〈S, ·,≤〉 with a binary operation · that is associative and a partial ordering ≤ that is compatible with the binary operation. For a given congruence relation θ of the semigroup S = 〈S, ·〉 the quotient structure S/θ = 〈S/θ, , 〉 is not in general an ordered semigroup. In this paper we study quotients of ordered semigroups. We first define a special type of ...

let tx be the full transformation semigroups on the set x. for an equivalence e on x, let te(x) = {α ∈ tx : ∀(x, y) ∈ e ⇔ (xα, yα) ∈ e}it is known that te(x) is a subsemigroup of tx. in this paper, we discussthe green's *-relations, certain *-ideal and certain rees quotient semigroup for te(x).