Power Exponents of Aperiodic Pseudovarieties
نویسنده
چکیده
This paper determines all pseudovarieties of nite semigroups whose powers are contained in DA. As an application, it is shown that it is computable, for a decidable pseudovariety V of aperiodic semigroups, the least exponent n such that the iterated power P n V is the pseudovariety of all nite semigroups.
منابع مشابه
Syntactic and Global Semigroup Theory, a Synthesis Approach
This paper is the culmination of a series of work integrating syntactic and global semigroup theoretical approaches for the purpose of calculating semidirect products of pseudovarieties of semigroups. We introduce various abstract and algorithmic properties that a pseudovariety of semi-groups might possibly satisfy. The main theorem states that given a nite collection of pseudovarieties, each s...
متن کاملThe linear nature of pseudowords
Given a pseudoword over suitable pseudovarieties, we associate to it a labeled linear order determined by the factorizations of the pseudoword. We show that, in the case of the pseudovariety of aperiodic finite semigroups, the pseudoword can be recovered from the labeled linear order.
متن کاملFinite Abundant Semigroups in Which the Idempotents Form a Subsemigroup*
We consider certain abundant semigroups in which the idempotents form a subsemigroup, and which we call bountiful semigroups. We find a simple criterion for a finite bountiful semigroup to be a member of the join of the pseudovarieties of finite groups and finite aperiodic semigroups.
متن کاملThe globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin
Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup B2, under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the level 3/2 of the refinement of Straubing-Thérien’s concatenation hierarchy introduced by...
متن کاملGeneral Hardy-Type Inequalities with Non-conjugate Exponents
We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...
متن کامل