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)
We prove that if π is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are π-groups. In particular, when π is the empty set, we obtain Henck-ell's decidability of aperiodic pointlikes. Our proof, restricted to the case of aperiodic semigroups, is simpler than the original proof.
We give a short proof, using profinite techniques, that idem-potent pointlikes, stable pairs and triples are decidable for the pseu-dovariety of aperiodic monoids. Stable pairs are also described for the pseudovariety of all finite monoids.
We generalize the holonomy form of the Prime Decomposition Theorem of Krohn and Rhodes for finite semigroups to arbitrary infinite semigroups. This is accomplished by embedding s^ into an infinite Zeiger wreath product after applying the triple Schiitzenberger product which makes S finite-J-above (Rhodes' theorem).
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)
ii ACKNOWLEDGEMENTS It's been quite a long journey through different undergraduate institutions, time off in the work force, and combining two majors to finally finish my bachelors degree. I thank my family for suffering through it all alongside me, and all the while giving constant encouragement and support for my decisions.
The Office of Graduate Studies has verified and approved the above named committee members. ii Dedicated to my parents, Bob and Sue Wood, and to my godmother, Dee Gelbach, for offering their love and support through everything I've done. Even the very silly things. iii ACKNOWLEDGEMENTS I owe a lot to a great many people for getting me this far. Ken… (More)