Related papers: Right regular triples of semigroups

Let $S,T$ be two numerical semigroups. We study when $S$ is one half of $T$, with $T$ almost symmetric. If we assume that the type of $T$, $t(T)$, is odd, then for any $S$ there exist infinitely many such $T$ and we prove that $1 \leq t(T)…

In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…

The multiplicative semigroup $M_n(F)$ of $n\times n$ matrices over a field $F$ is well understood, in particular, it is a regular semigroup. This paper considers semigroups of the form $M_n(S)$, where $S$ is a semiring, and the…

Cross-connection theory propounded by K. S. S. Nambooripad describes the ideal structure of a regular semigroup using the categories of principal left (right) ideals. A variant $\mathscr{T}_X^\theta$ of the full transformation semigroup…

A de Branges space $\mathcal B$ is regular if the constants belong to its space of associated functions and is symmetric if it is isometrically invariant under the map $F(z) \mapsto F(-z)$. Let $K_\mathcal{B}(z,w)$ be the reproducing kernel…

Let $G=\Gamma(S)$ be a semigroup graph, i.e., a zero-divisor graph of a semigroup $S$ with zero element 0. For any adjacent vertices $x, y$ in $G$, denote $C(x,y)={z\in V(G) | N(z)={x,y}}$. Assume that in $G$ there exist two adjacent…

In this paper we elaborate on the structure of the semigroup tree and the regularities on the number of descendants of each node observed earlier. These regularites admit two different types of behavior and in this work we investigate which…

Let $\mathcal{C}$ be a positive integer cone and $k\in \mathcal{C}$. A $\mathcal{C}$-semigroup $S$ is $k$-positioned if for every $h\in \mathcal{C}\setminus S$ we have that $k-h$ belongs to $S$. In this work, we focus on this family of…

Rational semigroups were introduced by Hinkkanen and Martin as a generalization of the iteration of a single rational map. There has subsequently been much interest in the study of rational semigroups. Quasiregular semigroups were…

The inclusion ideal graph $\mathcal{I}n(S)$ of a semigroup $S$ is an undirected simple graph whose vertices are all nontrivial left ideals of $S$ and two distinct left ideals $I, J$ are adjacent if and only if either $I \subset J$ or $J…

It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring $\mathbf{M}_n(S)$, of all $n\times n$ matrices over a…

In this paper, we characterize intra-regular LA-semihypergroups by using the properties of their left and right hyperideals and we investigate some useful conditions for an LA-semihypergroup to become an intra-regular LA-semihypergroup.

This paper considers numerical semigroups $S$ that have a non-principal relative ideal $I$ such that $\mu_S(I)\mu_S(S-I)=\mu_S(I+(S-I)) $. We show the existence of an infinite family of such which $I+(S-I)=S\backslash\{0\}$. We also show…

We find normal and seminormal forms for a sl(3)-valued zero curvature representation (ZCR). We prove a theorem about reducibility of ZCR's, which says that if one of the matrix in a ZCR (A,B) falls to a proper subalgebra of sl(3), then the…

We prove that an hypersemigroup $H$ is regular if and only, for any fuzzy subset $f$ of $H$, we have $f\preceq f\circ 1\circ f$ and it is intra-regular if and only if, for any fuzzy subset $f$ of $H$, we have $f\preceq 1\circ f\circ f\circ…

In this paper we present and study the numerical duplication of a numerical semigroup, a construction that, starting with a numerical semigroup $S$ and a semigroup ideal $E\subseteq S$, produces a new numerical semigroup, denoted by…

In this article we show that the semigroup operation of a strictly linearly ordered semigroup on a real interval is automatically continuous if each element of the semigroup admits a square root. Hence, by a result of Acz\'el, such a…

We describe a set $\mathcal{R}^{\infty}$ consisting of tuples of integer sequences and provide certain explicit maps on it. We show that this defines a semiregular crystal for $\mathfrak{sl}_{n+1}$ and $\mathfrak{sp}_{2n}$ respectively.…

A semiregular tree is a tree where all non-pendant vertices have the same degree. Belardo et al. (MATCH Commun. Math. Chem. 61(2), pp. 503-515, 2009) have shown that among all semiregular trees with a fixed order and degree, a graph with…

A class of groups is investigated, each of which has a fairly simple presentation . For example the group $R = (a, b, c, d | a^3 = b^3 = c^3 = d^3 = 1, ba^{-1} =dc^{-1}, ca^{-1} = db^{-1}) $ is in the class. Such a group does not have as a…