Related papers: On right $\pi$-inverse ordered semigroups
A reduction $\varphi$ of an ordered group $(G,P)$ to another ordered group is an order homomorphism which maps each interval $[1,p]$ bijectively onto $[1, \varphi(p)]$. We show that if $(G,P)$ is weakly quasi-lattice ordered and reduces to…
We establish key connections between Green's $\cal J$- and $\cal L$-relations on a finite semigroup and the subduction relation defined on the image sets of an action of the same semigroup when it acts faithfully on a finite set. The…
We determine when an orthodox semigroup S has a permutation that sends each member of S to one of its inverses and show that if such a permutation exists, it may be taken to be an involution. In the case of a finite orthodox semigroup the…
The paper is an overview of recent results on algebraic structures (semigroups, groupoids, algebras, inverse semigroups, and groups) associated with objects with a rich set of partial symmetries. We discuss etale groupoids and inverse…
In this paper we investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which admit a compact semigroup topology and describe graph…
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
A subcategory $\textbf{C}$ of a groupoid $\mathbb{G}$ is a left order in $\mathbb{G}$, if every element of $\mathbb{G}$ can be written as $a^{-1}b$ where $a, b \in \textbf{C}$. A subsemigroupoid $\mathfrak{C}$ of a groupoid $\mathbb{G}$ is…
Directed graphs have long been used to gain understanding of the structure of semigroups, and recently the structure of directed graph semigroups has been investigated resulting in a characterization theorem and an analog of Fruct's…
The classes of 1MP-inverses and MP1-inverses are recently introduced classes of generalized inverses of complex matrix. Actually, they coincide with the classes of $\{1,2,3\}$ and $\{1,2,4\}$ inverses, respectively. We consider these…
In this note we start the study of whether the reduced C*-algebra of an inverse semigroup is quasi-diagonal, making explicit use of the inner structure of this class of semigroups in order to produce quasi-diagonal approximations. Given a…
This paper pursues an investigation on groups equipped with an $L$-ordered relation, where $L$ is a fixed complete complete Heyting algebra. First, by the concept of join and meet on an $L$-ordered set, the notion of an $L$-lattice is…
Locally inverse semigroups are regular semigroups whose idempotents form pseudo-semilattices. We characterise the categories that correspond to locally inverse semigroups in the realm of Nambooripad's cross-connection theory. Further, we…
We reinterpret the Rhodes semilattices $R_n(\mathfrak{G})$ of a group $\mathfrak{G}$ in terms of gain graphs and generalize them to all gain graphs, both as sets of partition-potential pairs and as sets of subgraphs, and for the latter,…
This paper serves as an example to show the way we pass from ordered groupoids (ordered semigroups) to ordered hypergroupoids (ordered hypersemigroups), from groupoids (semigroups) to hypergroupoids (hypersemigroups). The results on…
'A semigroup is completely regular if and only if it is a union of groups'- an analogue of this structure theorem of completely regular semigroup has been obtained in the setting of seminearrings in [[16], Mukherjee (Pal) et al., Semigroup…
Given a semigroup S with zero, which is left-cancellative in the sense that st=sr \neq 0 implies that t=r, we construct an inverse semigroup called the inverse hull of S, denoted H(S). When S admits least common multiples, in a precise…
The first author has recently shown that semisimple algebraic groups are classified up to motivic equivalence by the local versions of the classical Tits indexes over field extensions, known as Tits p-indexes. We provide in this article the…
We consider semigroups of transformations (partial mappings defined on a set $A$) closed under the set-theoretic intersection of mappings treated as subsets of $A\times A$. On such semigroups we define two relations: the relation of…
In this paper we develop an ideal structure theory for the class of left reductive regular semigroups and apply it to several subclasses of popular interest. In these classes we observe that the right ideal structure of the semigroup is…
In this paper, we provide techniques to obtain left non-degenerate set-theoretic solutions of the Yang-Baxter equation, drawing on the class of right groups. To this end, we introduce the new algebraic structures of left $RG$-semibraces,…