On finitely related semigroups
نویسندگان
چکیده
An algebraic structure is finitely related (has finite degree) if its term functions are determined by some finite set of finitary relations. We show that the following finite semigroups are finitely related: commutative semigroups, 3-nilpotent monoids, regular bands, semigroups with a single idempotent, and Clifford semigroups. Further we provide the first example of a semigroup that is not finitely related: the 6-element Brandt monoid. This answers a question by Davey, Jackson, Pitkethly, and Szabó from Davey et al. (Semigroup Forum, 83(1):89–122, 2011).
منابع مشابه
Finitely Generated Weakly Reductive Commutative Semigroups∗
We give characterizations of the property of being weakly reductive for finitely generated commutative semigroups. As a consequence of these characterizations we obtain an algorithm for determining from a presentation of a finitely generated commutative semigroup whether it is weakly reductive. Furthermore, we present some connections between cancellative finitely generated commutative semigrou...
متن کاملAutomatic presentations for semigroups
This paper applies the concept of FA-presentable structures to semigroups. We give a complete classification of the finitely generated FA-presentable cancellative semigroups: namely, a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group. We prove that all finitely generated commutative semigroups are FA-presentable. We giv...
متن کاملPrincipal Ideals of Finitely Generated Commutative Monoids
We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.
متن کاملA Solvable Conjugacy Problem for Finitely Presented C(3) Semigroups
In his thesis, Remmers [R], introduced semigroup derivation diagrams and used them to prove that the word problem for finitely presented C(3) semigroups was solvable. In this article we introduce the annular analog of semigroup derivation diagrams and use them to demonstrate the solution to a conjugacy problem for finitely presented C(3) semigroups. Version of 5-21-2013
متن کاملThe equational theories of representable residuated semigroups
We show that the equational theory of representable lower semilattice-ordered residuated semigroups is finitely based. We survey related results.
متن کامل