Related papers: Partial Conway and iteration semirings

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…

Esik and Maletti introduced the notion of a proper semiring and proved that some important (classes of) semirings -- Noetherian semirings, natural numbers -- are proper. Properness matters as the equivalence problem for weighted automata…

This paper enriches the list of known properties of congruence sequences starting from the universal relation and successively performing the operators lower $k$ and lower $t$. Two series of inverse semigroups, namely…

Ara\'ujo, Kinyon and Konieczny (2011) pose several problems concerning the construction of arbitrary commuting graphs of semigroups. We observe that every star-free graph is the commuting graph of some semigroup. Consequently, we suggest…

We introduce a class of rings using which we define the concept of skew regularity for quaternion-valued functions over quaternions. It is shown that the notion of skew regularity coincides with the concept of slice regularity over…

We introduce an operator on classes of regular languages, the star-free closure. Our motivation is to generalize standard results of automata theory within a unified framework. Given an arbitrary input class $C$, the star-free closure…

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…

To any semigroup presentation $\mathcal{P}= \langle \Sigma \mid \mathcal{R} \rangle$ and base word $w \in \Sigma^+$ may be associated a nonpositively curved cube complex $S(\mathcal{P},w)$, called a Squier complex, whose underlying graph…

A numerical semigroup is a cofinite subset of the non-negative integers that is closed under addition and contains 0. Each numerical semigroup $S$ with fixed smallest positive element $m$ corresponds to an integer point in a rational…

We extend the definition and construct several bases for polylogarithms Li T , where T are some series, recognizable by a finite state (multiplicity) automaton of alphabet 4 X = {x 0 , x 1 }. The kernel of this new "polylogarithmic map" Li…

This paper summarizes results on some topics in the max-plus convex geometry, mainly concerning the role of multiorder, Kleene stars and cyclic projectors, and relates them to some topics in max algebra. The multiorder principle leads to…

An involution on a semigroup S (or any algebra with an underlying associative binary operation) is a function f:S->S that satisfies f(xy)=f(y)f(x) and f(f(x))=x for all x,y in S. The set I(S) of all such involutions on S generates a…

A semicrossed product is a non-selfadjoint operator algebra encoding the action of a semigroup on an operator or C*-algebra. We prove that, when the positive cone of a discrete lattice ordered abelian group acts on a C*-algebra, the…

We define the full and reduced non-self-adjoint operator algebras associated with \'etale categories and restriction semigroups, answering a question posed by Kudryavtseva and Lawson in \cite{lawson}. Moreover, we define the semicrossed…

Consider a pseudo-$H$-space $E$ endowed with a separately continuous biadditive associative multiplication which induces a grading on $E$ with respect to an abelian group $G$. We call such a space a graded pseudo-$H$-ring and we show that…

Loday's dendriform algebras and its siblings pre-Lie and zinbiel have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each individual…

An ordered semiring is a commutative semiring equipped with a compatible preorder. Ordered semirings generalise both distributive lattices and commutative rings, and provide a convenient framework to unify certain aspects of lattice theory…

This paper enriches the list of properties of the congruence sequences starting from the universal relation and successively performing the operations of lower $t$ and lower $k$. Three classes of completely regular semigroups, namely…

We introduce a version of probabilistic Kleene algebra with angelic nondeterminism and a corresponding class of automata. Our approach implements semantics via distributions over multisets in order to overcome theoretical barriers arising…

The aim of this series of papers is to study $z$-ideals of semirings. In this article, we introduce some distinguished classes of $z$-ideals of semirings, which include $z$-prime, $z$-semiprime, $z$-irreducible, and $z$-strongly irreducible…