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.
Bibliographical notePublisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Garside monoids
- Gaussian monoids
- lcm monoids
ASJC Scopus subject areas
- Algebra and Number Theory