Different commutative semigroups may have a common saturation. We consider distinguishing semigroups with a common saturation based on their “sparsity”. We propose to qualitatively describe sparsity of a semigroup by considering which faces of the corresponding rational polyhedral cone have saturation points. For a commutative semigroup we give a necessary and sufficient condition for determini...

We construct explicitly regular sequences in the semigroup ring R = C[K] of lattice points of the graded cone K. We conjecture that the quotients of R by these sequences describe locally string-theoretic cohomology of a toroidal singularity associated to K. As a byproduct, we give an elementary proof of the result of Hochster that semigroup rings of rational polyhedral cones are Cohen-Macaulay.

Semi-graphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the reflection arrangement of the symmetric group Sn. In this paper we resolve two problems on semi-graphoids posed in Studený’s book [19], and we answer a related question of Postnikov, Reiner, and Williams on generalized permutohed...

This is an expository article whose main aim is to introduce nor~nal affine semigroups and its links with other areas such as graph tlleory, linear programming and polyhedral geometry. As an application we derive the classical and generalized ~narriage theorems. 1 Introduction Let A = (a i j) be an integral matrix of order n x q with nonzero distinct columns and let A = {vl,. .. ,v,) be the set...

Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of ...

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.

Given an integer matrix $A\in\Bbb{Z}^{d\times n}$, we study the natural mixed Hodge module structure in sense of Saito on Gau\ss--Manin system attached to monomial map $h\colon(\Bbb{C}^*)^d\to\Bbb{C}^n$ induced by $A$. We completely determine normal case associated graded object weight filtration, computing intersection complexes with respective multiplicities that form its constituents. Our re...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.