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Perfect Amalgamation Bases

Perfect Amalgamation Bases
Perfect Amalgamation Bases
In [6], 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.
amalgamation, semigroups, monoids, S-act flatness, perfect
0021-8693
78-92
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c

Renshaw, James (1991) Perfect Amalgamation Bases. Journal of Algebra, 141 (1), 78-92. (doi:10.1016/0021-8693(91)90204-L).

Record type: Article

Abstract

In [6], 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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More information

Published date: 1991
Keywords: amalgamation, semigroups, monoids, S-act flatness, perfect

Identifiers

Local EPrints ID: 41106
URI: http://eprints.soton.ac.uk/id/eprint/41106
DOI: doi:10.1016/0021-8693(91)90204-L
ISSN: 0021-8693
PURE UUID: 35efe04e-91dc-4681-9adf-8f450921a6ea
ORCID for James Renshaw: ORCID iD orcid.org/0000-0002-5571-8007

Catalogue record

Date deposited: 19 Jul 2006
Last modified: 16 Mar 2024 02:39

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Author: James Renshaw ORCID iD

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