ACTA issues

Simplified conditions for type-I and type-II monoids

Christopher Hollings

Acta Sci. Math. (Szeged) 77:1-2(2011), 63-72

Abstract. In a previous paper, we obtained conditions on a monoid $M$ for its prefix expansion to be either a left restriction monoid (in which case $M$ must be either `type-I' or `type-II') or a left ample monoid ($M$ is `type-Ia' or `type-IIa'). In the present paper, we demonstrate that there is some redundancy in these conditions. We therefore trim down the sets of conditions and show, by construction of suitable counterexamples, that the reduced sets of conditions are independent.

AMS Subject Classification (1991): 20M99

Keyword(s): monoid, unipotent, bipotent, type-I, type-II, type-Ia, type-IIa

Received September 1, 2009, and in final form January 14, 2010. (Registered under 99/2009.)