Related papers: Cross-connections of the singular transformation s…
In order to simultaneously generalize matrix rings and group graded crossed products, we introduce category crossed products. For such algebras we describe the center and the commutant of the coefficient ring. We also investigate the…
A partial automorphism of a semigroup $S$ is any isomorphism between its subsemigroups, and the set all partial automorphisms of $S$ with respect to composition is the inverse monoid called the partial automorphism monoid of $S$. Two…
In the following text we introduce the concept of pseudo-codecomposition of a transformation group, also we show the collection of all transformation groups pseudo-codecomposable to distal ones is a proper intermediate class of the class of…
We give a thorough structural analysis of the principal one-sided ideals of arbitrary semigroups, and then apply this to full transformation semigroups and symmetric inverse monoids. One-sided ideals of these semigroups naturally occur as…
Consider an algebraic variety $X$ over a base scheme $S$ and a faithful base change $T \to S$. Given an admissible subcategory $\CA$ in the bounded derived category of coherent sheaves on $X$, we construct an admissible subcategory in the…
We develop a semigroup-theoretic analogue of liaison for relative ideals of a numerical semigroup. Two parallel linkage notions are proposed: a theory based on translates of the semigroup and a theory based on translates of the canonical…
We revise the notion of the quasi-sectorial contractions. Our main theorem establishes a relation between semigroups of quasi-sectorial contractions and a class of m-sectorial generators. We discuss a relevance of this kind of contractions…
A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…
This paper concerns the general problem of classifying the finite deterministic automata that admit a synchronizing (or reset) word. (For our purposes it is irrelevant if the automata has initial or final states.) Our departure point is the…
We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is…
Suppose that $\alpha$ is an action of the semigroup $\mathbb{N}^{2}$ on a $C^*$-algebra $A$ by endomorphisms. Let $A\times_{\alpha}^{\textrm{piso}} \mathbb{N}^{2}$ be the associated partial-isometric crossed product. By applying an earlier…
Given a semigroup $S$ and $s,t \in S$, write $s \sim_p^1 t$ if $s=pr$ and $t=rp$, for some $p,r \in S \cup \{1\}$. This relation, known as "primary conjugacy", along with its transitive closure $\sim_p$, has been extensively used and…
This paper touches on several interaction points of semigroups and constructions from category theory: An adjunction is established between categories with selected arrows and semigroups. Regular semigroups are characterized by split epi -…
This paper is devoted to characterizing the so-called order isomorphisms intertwining the $L^2$-semigroups of two Dirichlet forms. We first show that every unitary order isomorphism intertwining semigroups is the composition of…
A graded tensor category over a group $G$ will be called a crossed product tensor category if every homogeneous component has at least one multiplicatively invertible object. Our main result is a description of the crossed product tensor…
For a given inverse semigroup S , we introduce the notion of algebraic crossed product by using a given partial action of S, and we will prove that under some condition it is associative. Also we will introduce the concept of partial…
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 generalise the concept of a Steinberg cross-section to non-connected Kac-Moody group. As in the connected case, which was treated by G. Br\"uchert, a quotient map w.r.t the conjugacy action exists only on a certain submonoid of the…
We show that for any discrete semigroup $X$ the semigroup operation can be extended to a right-topological semigroup operation on the space $G(X)$ of inclusion hyperspaces on $X$. We detect some important subsemigroups of $G(X)$, study the…
A cross matrix $X$ can have nonzero elements located only on the main diagonal and the anti-diagonal, so that the sparsity pattern has the shape of a cross. It is shown that $X$ can be factorized into products of matrices that are at most…