Embedding Boolean Ample Monoids as Full Submonoids of Boolean Inverse Monoids

Mark V. Lawson

doi:10.1017/S0004972726101634

Embedding Boolean Ample Monoids as Full Submonoids of Boolean Inverse Monoids

Mark V. Lawson

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

Abstract

We show that, in certain circumstances, a Boolean ample monoid may be fully embedded into a Boolean inverse monoid in a way that generalises how right reversible cancellative monoids may be embedded into groups. We use groupoids of fractions and noncommutative Stone duality to prove the result.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Bulletin of the Australian Mathematical Society
Early online date	22 Jul 2026
DOIs	https://doi.org/10.1017/S0004972726101634
Publication status	E-pub ahead of print - 22 Jul 2026

Keywords

ample monoid
inverse monoid
groupoid of fractions
Boolean restriction monoid
Stone duality

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10.1017/S0004972726101634

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title = "Embedding Boolean Ample Monoids as Full Submonoids of Boolean Inverse Monoids",

abstract = "We show that, in certain circumstances, a Boolean ample monoid may be fully embedded into a Boolean inverse monoid in a way that generalises how right reversible cancellative monoids may be embedded into groups. We use groupoids of fractions and noncommutative Stone duality to prove the result.",

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AB - We show that, in certain circumstances, a Boolean ample monoid may be fully embedded into a Boolean inverse monoid in a way that generalises how right reversible cancellative monoids may be embedded into groups. We use groupoids of fractions and noncommutative Stone duality to prove the result.

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KW - inverse monoid

KW - groupoid of fractions

KW - Boolean restriction monoid

KW - Stone duality

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JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

ER -

Embedding Boolean Ample Monoids as Full Submonoids of Boolean Inverse Monoids

Abstract

Keywords

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