Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions

Alan James Cain; Edmund Frederick Robertson; Nik Ruskuc

doi:10.1017/S1446788708000086

Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions

Alan James Cain, Edmund Frederick Robertson, Nik Ruskuc

Research output: Contribution to journal › Article › peer-review

Abstract

It is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative and right-cancellative presentations. (A Malcev (respectively, cancellative, left-cancellative, right-cancellative) presentation is a presentation of a special type that can be used to define any group-embeddable (respectively, cancellative, left-cancellative, right-cancellative) semigroup.).

Original language	English
Pages (from-to)	39-61
Number of pages	23
Journal	Journal of the Australian Mathematical Society
Volume	84
Issue number	1
DOIs	https://doi.org/10.1017/S1446788708000086
Publication status	Published - Feb 2008

Keywords

Maclev presentation
Cancellative
Subsemigroup
Finite index
Rewriting

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10.1017/S1446788708000086

JAustMathSoc84CancellativeMalcevPresentations
(c) 2008 Australian Mathematical Society
Final published version, 213 KB

Cite this

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title = "Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions",

abstract = "It is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative and right-cancellative presentations. (A Malcev (respectively, cancellative, left-cancellative, right-cancellative) presentation is a presentation of a special type that can be used to define any group-embeddable (respectively, cancellative, left-cancellative, right-cancellative) semigroup.).",

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author = "Cain, \{Alan James\} and Robertson, \{Edmund Frederick\} and Nik Ruskuc",

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AU - Robertson, Edmund Frederick

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N2 - It is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative and right-cancellative presentations. (A Malcev (respectively, cancellative, left-cancellative, right-cancellative) presentation is a presentation of a special type that can be used to define any group-embeddable (respectively, cancellative, left-cancellative, right-cancellative) semigroup.).

AB - It is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative and right-cancellative presentations. (A Malcev (respectively, cancellative, left-cancellative, right-cancellative) presentation is a presentation of a special type that can be used to define any group-embeddable (respectively, cancellative, left-cancellative, right-cancellative) semigroup.).

KW - Maclev presentation

KW - Cancellative

KW - Subsemigroup

KW - Finite index

KW - Rewriting

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Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions

Abstract

Keywords

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EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications

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Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

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EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications

Cite this