Perfect Amalgamation Bases.
Journal of Algebra, 141, (1), . (doi:10.1016/0021-8693(91)90204-L).
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In , Howie considered the following problem: If [U; Si] is an amalgam of semigroups and if Ti are subsemigroups of Si such that [U; Ti]is an amalgam, is it true that ?U* Ti, the free product of the amalgam [U; Ti], is embeddable in ?U* Si the free product of the amalgam [U; Si]? He proved, among other things, that if U and Ti are unitary in Si, then the free products are embeddable.
We extend these results here using the homological techniques introduced in [4, 7]and culminate in describing those amalgamation bases which always have this property.
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