Related papers: Relational depth of transformation semigroups and …

The shedding vertices of simplicial complexes are studied from an algebraic point of view. Based on this perspective, we introduce the class of ass-decomposable monomial ideals which is a generalization of the class of Stanley-Reisner…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

Pursuing ideas of Jeff Smith, we develop a homotopy theory of ideals of monoids in a symmetric monoidal model category. This includes Smith ideals of structured ring spectra and of differential graded algebras. Such Smith ideals are NOT…

The dead-end depth of an element g of a group G, with respect to a generating set A is the distance from g to the complement of the radius $d_A(1,g)$ closed ball, in the word metric $d_A$ defined with respect to A. We exhibit a finitely…

We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…

Let $S$ be a polynomial algebra over a field. We study classes of monomial ideals (as for example lexsegment ideals) of $S$ having minimal depth. In particular, Stanley's conjecture holds for these ideals. Also we show that if Stanley's…

Let $\mathcal C \subset \mathbb N^p$ be a finitely generated integer cone and $S\subset \mathcal C$ be an affine semigroup such that the real cones generated by $\mathcal C$ and by $S$ are equal. The semigroup $S$ is called $\mathcal…

In this paper we show that the Stanley depth, as well as the usual depth, are essentially determined by the lcm-lattice. More precisely, we show that for quotients $I/J$ of monomial ideals $J\subset I$, both invariants behave monotonic with…

We determine the structure of the intersection of a finitely generated subgroup of a semiabelian variety $G$ defined over a finite field with a closed subvariety $X\subset G$.

The intersection ideal graph $\Gamma(S)$ of a semigroup $S$ is a simple undirected graph whose vertices are all nontrivial left ideals of $S$ and two distinct left ideals $I, J$ are adjacent if and only if their intersection is nontrivial.…

The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…

In this paper the concept of extension of a Q-fuzzy ideal in semigroups has been introduced and some important properties have been studied.

In this paper, we study defining ideals of numerical semigroup rings. Let $H$ be a numerical semigroup with multiplicity $a_0$ and embedding dimension $n$. Assuming $a_0/2+1\leq n$, we prove that the defining ideal of $H$ is determinantal…

Let $I$ be a squarefree monomial ideal of a polynomial algebra over a field minimally generated by $f_1,...,f_r$ of degree $ d\geq 1$, and a set $E$ of monomials of degree $\geq d+1$. Let $J\subsetneq I$ be a squarefree monomial ideal…

The class of nil-essential ideals is a generalisation of the class of essential ideals. Every nil-essential ideal of a reduced ring is essential. Therefore the intersection of all nil-essential ideals over a reduced ring $R$ is the socle of…

This paper continues the study of Fourier transforms on finite inverse semigroups, with a focus on Fourier inversion theorems and FFTs for new classes of inverse semigroups. We begin by introducing four inverse semigroup generalizations of…

Let $\mathbb{K}$ be a field and $S=\mathbb{K}[x_1,\dots,x_n]$ be the polynomial ring in $n$ variables over $\mathbb{K}$. Let $G$ be a graph with $n$ vertices. Assume that $I=I(G)$ is the edge ideal of $G$ and $J=J(G)$ is its cover ideal. We…

We develop a new technique for studying monomial ideals in the standard polynomial rings $A[X_1,\ldots,X_d]$ where $A$ is a commutative ring with identity. The main idea is to consider induced ideals in the semigroup ring…

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…

Let $\mathcal{PORD}_{n}$ be the semigroup consisting of all oriented and order-decreasing partial transformations on the finite chain $X_{n}=\{ 1<\cdots<n \}$. Let $\mathcal{IORD}_{n}$ be the subsemigroup of $\mathcal{PORD}_{n}$ consisting…