Cancellative semigroup

About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.

The quotient of a numerical semigroup by a positive integer

Abstract: A generalization of the linear Diophantine Frobenius problem can be stated as follows. Let n 1 ,…,n p and d be positive integers with {n 1 ,…,n p }=1. Find a formula for the largest multiple of d not belonging to 〈n 1 ,…,n p 〉.

On disjunction of equations in the semigroup language with no constants

Abstract: A semigroup S is an equational domain if any finite union of algebraic sets over S is algebraic. We prove that every nontrivial semigroup in the standard language {·} is not an equational domain.

Restriction of Markov Integrated Semigroups and Generation of Increasing Integrated semigroups

Abstract: We prove that the transition function is a positive contraction C_0 semigroup on a subspace C1 of l_∞. We obtain that the generator of the Markov integrated semigroup is densely defined in l_∞ if and only if q-matrix Q is uniformly bounded. At the same time, a sufficient and necessary condition for a transition function to a Feller-Reuter-Riley transition function, is also given. Finally, in an ordered Banach space, a generation theorem is obtained for the increasing integrated semigroup of contractions.

Locally Adequate Semigroups Satisfying the Regularity Condition

Abstract: The aim of this paper is to study locally adequate semigroups with the regularity condition. We prove that an abundant semigroup is a locally adequate semigroup with the regularity condition if and only if it is a local E-isomorphic image of an abundant Rees matrix semigroup over an adequate semigroup, each entry of the sandwich matrix of which is regular. This extends the results of M V Lawson and D B McAlister.