A note on Garside monoids and $${\mathscr {M}}$$-braces

Fabienne Chouraqui

doi:10.1007/s00233-023-10344-3

A note on Garside monoids and $${\mathscr {M}}$$-braces

Fabienne Chouraqui

Faculty of Natural Sciences

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

Abstract

We define an algebraic structure similar to that of a semiring, but without some of the requirements. As it is somehow also similar to the structure of left brace, we call it an M-brace. We present a connection between Garside monoids and more generally lcm-monoids with this algebraic structure. An lcm-monoid M is a left-cancellative monoid such that 1 is the unique invertible element in M, and every pair of elements in M admit an lcm with respect to left-divisibility. The class of lcm-monoids contains the Gaussian, quasi-Garside and Garside monoids.

Original language	English
Journal	Semigroup Forum
DOIs	https://doi.org/10.1007/s00233-023-10344-3
State	Accepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

braces
Garside monoids
Gaussian monoids
lcm monoids

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s00233-023-10344-3

Cite this

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AB - We define an algebraic structure similar to that of a semiring, but without some of the requirements. As it is somehow also similar to the structure of left brace, we call it an M-brace. We present a connection between Garside monoids and more generally lcm-monoids with this algebraic structure. An lcm-monoid M is a left-cancellative monoid such that 1 is the unique invertible element in M, and every pair of elements in M admit an lcm with respect to left-divisibility. The class of lcm-monoids contains the Gaussian, quasi-Garside and Garside monoids.

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A note on Garside monoids and $${\mathscr {M}}$$-braces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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