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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Amalgamation for inverse and generalized inverse semigroups


Author: T. E. Hall
Journal: Trans. Amer. Math. Soc. 310 (1988), 313-323
MSC: Primary 20M10; Secondary 08B25, 20M17, 20M18
MathSciNet review: 965756
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0965756-7
PII: S 0002-9947(1988)0965756-7
Article copyright: © Copyright 1988 American Mathematical Society