A note on identities in two variables for a class of monoids

Enrique Salcido and Emil Daniel Schwab
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 1, Pages 86–92
DOI: 10.7546/nntdm.2020.26.1.86-92
Full paper (PDF, 178 Kb)

Details

Authors and affiliations

Enrique Salcido
MS student, Department of Mathematical Sciences, The University of Texas at El Paso
El Paso, Texas 79968, USA

Emil Daniel Schwab
Department of Mathematical Sciences, The University of Texas at El Paso
El Paso, Texas 79968, USA

Abstract

In this note we consider identities in the alphabet X = {x, y}. This note is self-contained and the aim is to describe gradually the identities partition (with three parameters) of the free semigroup X⁺ for the class of monoids B_n = {a, b | ba = bⁿ} (n > 0).

Keywords

• Semigroup identities
• Checking identities
• Identities partition

2010 Mathematics Subject Classification

• 68R15
• 08A50

References

1. Adjan, S.I. (1967). Defining relations and algorithmic problems for groups and semigroups, American Mathematical Society, Providence, (English translation of Proceeding of the Steklov Institute of Mathematics Vol. 85).
2. Geroldinger, A. & Schwab, E. D. (2018). Sets of lengths in atomic unit-cancellative finitely presented monoids, Colloq. Math., 151, 171–187.
3. Pastijn, F. (2006). Polyhedral convex cones and the equational theory of the bicyclic semigroup, J. Aust. Math. Soc., 81, 63–96.
4. Shleifer, F. G. (1990). Looking for identities on a bicyclic semigroup with computer assistance, Semigroup Forum, 41, 173–179.
5. Shneerson, L. M. (1985). On the varieties generated by semigroups and monoids with one defining relation, Siberian Math. Journal 26, 202 (Abstract), Preprint VINITI No 3641–84, 1–32.