Amalgamation for inverse and generalized inverse semigroups

Hall, T. E.

doi:10.1090/S0002-9947-1988-0965756-7

Amalgamation for inverse and generalized inverse semigroups
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Trans. Amer. Math. Soc. 310 (1988), 313-323 Request permission

Abstract:

For any amalgam $(S, T; U)$ of inverse semigroups, it is shown that the natural partial order on $S{{\ast }_U}T$, the (inverse semigroup) free product of $S$ and $T$ amalgamating $U$, has a simple form on $S \cup T$. In particular, it follows that the semilattice of $S{{\ast }_U}T$ is a bundled semilattice of the corresponding semilattice amalgam $(E(S), E(T); E(U))$; taken jointly with a result of Teruo Imaoka, this gives that the class of generalized inverse semigroups has the strong amalgamation property. Preserving finiteness is also considered.

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