Neutrices and external numbers were proposed as models of orders of magnitude within nonstandard analysis. We show that the external numbers form a commutative regular semigroup for addition and that the external numbers which are not neutrices form a commutative regular semigroup for multiplication. The validity of the distributive law is restricted, but it can be fully characterized. 2000 Mat...

With the usual notation for congruences on a regular semigroup S, in a previous communication we studied the lattice Λ generated by Γ = {σ, τ, μ, β} relative to properties such as distributivity and similar conditions. For K and T the kernel and trace relations on the congruence lattice of S, we form an abstraction of the triple (Λ;K|Λ, TΛ) called a c-triple. In this study a number of relations...

Abstract. In this paper, we introduce generalized fuzzy weakly interior ideals of an ordered semigroup. We generalize fuzzy interior ideals of an ordered semigroup. We establish necessary and sufficient condition for a fuzzy set to be a generalized fuzzy weakly interior ideal. We establish three equivalent conditions for an ordered semigroup to be regular. We characterize semisimple ordered sem...

A common generalization of the author's embedding theorem concerning the £-unitary regular semigroups with regular band of idempotents, and Billhardt's and Ismaeel's embedding theorem on the inverse semigroups, the closure of whose set of idempotents is a Clifford semigroup, is presented. We prove that each orthodox semigroup with a regular band of idempotents, which is an extension of an ortho...

Let X be a chain, OP (X) the order-preserving partial transformation semigroup on X and OI(X) the order-preserving 1–1 partial transformation semigroup on X. It is known that both OP (X) and OI(X) are regular semigroups. We extend these results by characterizing the regular elements of the semigroups OP (X,Y ), OI(X,Y ), OP (X,Y ) and OI(X,Y ) where ∅ = Y ⊆ X,OP (X,Y ) = {α ∈ OP (X) | ranα ⊆ Y ...

In this paper, we introduce a generalized class of an Hv-semigroup obtained from an LA-semigroup H. This generalized Hv-structure is called an Hv-LA-semigroup. We provide several examples of Hv-LA-semigroups. Moreover, with the help of an example we obtain that each LA-semigroup endowed with an equivalence relation can induce an Hv-LA-semigroup. We also investigate isomorphism theorems with the...

Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancell...

Let E be a product system of C-correspondences over Nr 0 . Some sufficient conditions for the existence of a not necessarily regular isometric dilation of a completely contractive representation of E are established and difference between regular and -regular dilations discussed. It is in particular shown that a minimal isometric dilation is -regular if and only if it is doubly commuting. The c...

A semigroup whose bi-ideals and quasi-ideals coincide is called a -semigroup. The full transformation semigroup on a set X and the semigroup of all linear transformations of a vector space V over a field F into itself are denoted, respectively, by T(X) and LF(V). It is known that every regular semigroup is a -semigroup. Then both T(X) and LF(V) are -semigroups. In 1966, Magill introduced and st...