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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.
Acknowledgments
The second author thanks Department of Mathematics, Monash University for its hospitality during the first six months of 1998, while the joint research was being done.