On the number of subsemigroups of direct products involving the free monogenic semigroup

Ashley Clayton; Nikola Ruskuc

doi:10.1017/S1446788718000605

On the number of subsemigroups of direct products involving the free monogenic semigroup

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

Abstract

The direct product ℕ x ℕ of two free monogenic semigroups contains uncountably many pairwise nonisomorphic subdirect products. Furthermore, the following hold for ℕ x S, where S is a finite semigroup. It contains only countably manypairwise non-isomorphic subsemigroups if and only if S is a union of groups. And it contains only countably many pairwise nonisomorphic subdirect products if and only if every element of S has a relative left or right identity element.

Original language	English
Pages (from-to)	24-35
Number of pages	12
Journal	Journal of the Australian Mathematical Society
Volume	109
Issue number	1
Early online date	1 Feb 2019
DOIs	https://doi.org/10.1017/S1446788718000605
Publication status	Published - 1 Aug 2020

Keywords

Subdirect product
Subsemigroup
Free mongenic semigroup

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10.1017/S1446788718000605

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© 2019 Australian Mathematical Publishing Association Inc. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/S1446788718000605
Accepted author manuscript, 299 KBLicence: Unspecified

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AB - The direct product ℕ x ℕ of two free monogenic semigroups contains uncountably many pairwise nonisomorphic subdirect products. Furthermore, the following hold for ℕ x S, where S is a finite semigroup. It contains only countably manypairwise non-isomorphic subsemigroups if and only if S is a union of groups. And it contains only countably many pairwise nonisomorphic subdirect products if and only if every element of S has a relative left or right identity element.

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KW - Subsemigroup

KW - Free mongenic semigroup

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On the number of subsemigroups of direct products involving the free monogenic semigroup

Abstract

Keywords

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Subdirect products of free semigroups and monoids

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On the number of subsemigroups of direct products involving the free monogenic semigroup

Abstract

Keywords

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Student theses

Subdirect products of free semigroups and monoids

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