Karsten Henckell

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This paper is concerned with the many deep and far reaching consequences of Ash’s positive solution of the type II conjecture for finite monoids. After rewieving the statement and history of the problem, we show how it can be used to decide if a finite monoid is in the variety generated by the Malcev product of a given variety and the variety of groups.(More)
In this paper we give a new proof of the following result of Straubing and Thérien: every J -trivial monoid is a quotient of an ordered monoid satisfying the identity x ≤ 1. We will assume in this paper that the reader has a basic background in finite semigroup theory (in particular, Green’s relations and identities defining varieties) and in computer(More)
Herein we generalize the holonomy theorem for finite semigroups (see [7]) to arbitrary semigroups, S, by embedding s^ into an infinite Zeiger wreath product, which is then expanded to an infinite iterative matrix semigroup. If S is not finite-J-above (where finite-J-above means every element has only a finite number of divisors), then S is replaced by g3,(More)
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