FINITE BANDS AND AMALGAMATION BASES FOR FINITE SEMIGROUPS

Abstract

ABSTRACT Hall and Putcha proved that if a finite semigroup S is an amalgamation base for all finite semigroups, then the -classes of S are linearly ordered. Oknin´ski and Putcha proved that any finite semigroup S is an amalgamation base for all finite semigroups if the -classes of are linearly ordered and the semigroup algebra over the complex field has a zero Jacobson radical. In this paper, we study the structure of semigroups which are amalgamation bases for all finite semigroups. In particular, the structure of finite bands which are amalgamation bases for all finite semigroups is determined.