Related papers: On proportionally modular numerical semigroups tha…

In this paper we compute the rank and exhibit a presentation for the monoids of all $P$-stable and $P$-order preserving partial permutations on a finite set $\Omega$, with $P$ an ordered uniform partition of $\Omega$. These (inverse)…

It was noticed recently that, given a metric space $(X,d_X)$, the equivalence classes of metrics on the disjoint union of the two copies of $X$ coinciding with $d_X$ on each copy form an inverse semigroup $M(X)$ with respect to…

Consider an algebraic semigroup $S$ and its closed subscheme of idempotents, $E(S)$. When $S$ is commutative, we show that $E(S)$ is finite and reduced; if in addition $S$ is irreducible, then $E(S)$ is contained in a smallest closed…

There exist two different sorts of gaps in the nonsymmetric numerical additive semigroups finitely generated by a minimal set of positive integers {d_1,...,d_m}. The h-gaps are specific only for the nonsymmetric semigroups while the g-gaps…

We characterise the numerical semigroups with a monotone Ap\'ery set (MANS-semigroups for abbreviate). Moreover, we describe the families of MANS-semigroups when we set the multiplicity and the ratio.

Commutative totally ordered monoids abound, number systems for example. When the monoid is not assumed commutative, one may be hard pressed to find an example. One suggested by Professor Orr Shalit are the countable ordinals with addition.…

Every semigroup containing an ideal subgroup is called a homogroup, and it is a grouplike if and only if it has only one central idempotent. On the other hand, a class of algebraic structures covering group-$e$-semigroups…

The notion of almost symmetric numerical semigroup was given by V. Barucci and R. Fr\"oberg. We characterize almost symmetric numerical semigroups by symmetry of pseudo-Frobenius numbers. We give a criterion for $H^*$ (the dual of $M$) to…

A semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities having real coefficients and is a union of finitely many maximally connected components. We consider the problem of deciding whether two…

The aim of this article is to study the ideal class monoid $\mathcal{C}\ell(S)$ of a numerical semigroup $S$ introduced by V. Barucci and F. Khouja. We prove new bounds on the cardinality of $\mathcal{C}\ell(S)$. We observe that…

Every numerical semigroup can be expressed as an intersection of irreducible numerical semigroups. We show that the unions of sets of lengths of factorizations of numerical semigroups into irreducible numerical semigroups are all equal to…

Let $\mathbb{A} = (A, \cdot)$ be a semigroup. We generalize some recent results by G. A. Freiman, M. Herzog and coauthors on the structure theory of set addition from the context of linearly orderable groups to linearly orderable…

Let G be a finite group that acts on an abelian monoid A. If f: A -> G is a map so that f(a f(a)(b)) = f(a)f(b), for all a, b in A, then the submonoid S = {(a, f(a)) | a in A} of the associated semidirect product of A and G is said to be a…

A (v,b,r,k) combinatorial configuration is a (r,k)-biregular bipartite graph with v vertices on the left and b vertices on the right and with no cycle of length 4. Combinatorial configurations have become very important for some…

Certain $*$-semigroups are associated with the universal $C^*$-algebra generated by a partial isometry, which is itself the universal $C^*$-algebra of a $*$-semigroup. A fundamental role for a $*$-structure on a semigroup is emphasized, and…

In this paper we study the structure of the monoid $\mathbf{I}\mathbb{N}_{\infty}^n$ of cofinite partial isometries of the $n$-th power of the set of positive integers $\mathbb{N}$ with the usual metric for a positive integer $n\geqslant…

A semi-dualizing module over a commutative noetherian ring A is a finitely generated module C with RHom_A(C,C) \simeq A in the derived category D(A). We show how each such module gives rise to three new homological dimensions which we call…

Let $[n]$ be a finite chain $\{1, 2, \ldots, n\}$, and let $\mathcal{LS}_{n}$ be the semigroup consisting of all isotone and order-decreasing partial transformations on $[n]$. Moreover, let $\mathcal{SS}_{n} = \{\alpha \in \mathcal{LS}_{n}…

Combinatorics on multisets is used to deduce new upper and lower bounds on the number of numerical semigroups of each given genus, significantly improving existing ones. In particular, it is proved that the number $n_g$ of numerical…

We derive polynomial identities of arbitrary degree $n$ for syzygies degrees of numerical semigroups S_m=<d_1,...,d_m> and show that for n>=m they contain higher genera G_r=\sum_{s\in Z_>\setminus S_m}s^r of S_m. We find a number…