Related papers: Semigroups of I-type

Weierstrass semigroups are well-known along the literature. We present a new family of non-Weierstrass semigroups which can be written as an intersection of Weierstrass semigroups. In addition, we provide methods for calculating…

Let $X$ be a nonempty set and $\mathcal{P}=\{X_i\colon i\in I\}$ be a partition of $X$. Denote by $T(X, \mathcal{P})$ the semigroup of all transformations of $X$ that preserve $\mathcal{P}$. In this paper, we study the semigroup…

A subset $S$ of an integral domain is called a semidomain if the pairs $(S,+)$ and $(S\setminus\{0\}, \cdot)$ are commutative and cancellative semigroups with identities. The multiplication of $S$ extends to the group of differences…

We solve a problem of Komeda concerning the proportion of numerical semigroups which do not satisfy Buchweitz' necessary criterion for a semigroup to occur as the Weierstrass semigroup of a point on an algebraic curve. We also show that the…

Let $f_1(n), \ldots, f_k(n)$ be polynomial functions of $n$. For fixed $n\in\mathbb{N}$, let $S_n\subseteq \mathbb{N}$ be the numerical semigroup generated by $f_1(n),\ldots,f_k(n)$. As $n$ varies, we show that many invariants of $S_n$ are…

The syntactic semigroup problem is to decide whether a given finite semigroup is syntactic or not. This work investigates the syntactic semigroup problem for both the semigroup reducts of $A^+(B_n)$, the affine near-semiring over a Brandt…

We define the concentration of a numerical semigroup $S$ as $\mathsf{C}(S)=\max \left\{\text{next}_S(s)-s ~|~ s\in S \backslash \{0\}\right\}$ wherein $\text{next}_S(s)=\min\left\{x \in S ~|~ s<x\right\}$. In this paper, we study the class…

Let A be a commutative Banach algebra such that uA = {0} for u $\in$ A \ {0} which possesses dense principal ideals. The purpose of the paper is to give a general framework to define F (--$\lambda$1$\Delta$T 1 ,. .. , --$\lambda$ k…

Let R: V x V -> V x V be a Hecke type solution of the quantum Yang-Baxter equation (a Hecke symmetry). Then, the Hilbert-Poincre' series of the associated R-exterior algebra of the space V is a ratio of two polynomials of degree m…

We define the notion of a semicharacter of a group G : A function from the group to C*, whose restriction to any abelian subgroup is a homomorphism. We conjecture that for any finite group, the order of the group of semicharacters is…

We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters…

We construct many irreducible polynomials within semigroups generated by sets of the form $S=\{x^2+c_1,\dots,x^2+c_s\}$ under composition.

For every group $G$, the set $\mathcal{P}(G)$ of its subsets forms a semiring under set-theoretical union $\cup$ and element-wise multiplication $\cdot$ and forms an involution semigroup under $\cdot$ and element-wise inversion ${}^{-1}$.…

We use the description of the Schutzenberger automata for amalgams of finite inverse semigroups given by Cherubini, Meakin, Piochi to obtain structural results for such amalgams. Schutzenberger automata, in the case of amalgams of finite…

This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…

We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski dense.…

We introduce the notion of $\imath$Schur superalgebra, which can be regarded as a type B/C counterpart of the $q$-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed $q$-permutation modules over Hecke…

An element e of an ordered semigroup $(S,\cdot,\leq)$ is called an ordered idempotent if $e\leq e^2$. We call an ordered semigroup $S$ idempotent ordered semigroup if every element of $S$ is an ordered idempotent. Every idempotent semigroup…

This paper is devoted to the presentation of combinatorial bialgebras whose coproduct is defined with the help of a commutative semigroup. We consider this setting in order to give a general framework which admits as special cases 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…