Tara Brough

Tara Brough (CMA, Universidade Nova de Lisboa)

Cross-sections and direct products of monoids:

Algebra and Geometry Seminar

6th December 2018, 4:30 pm – 5:30 pm
Howard House, 4th Floor Seminar Room

A cross-section (or set of normal forms) for a monoid M is a language (over some generating set for M) of unique representatives for elements of M.
A monoid is Markov if it has a prefix-closed regular cross-section over some generating set.

I will give an example of a monoid M that has no regular cross-section, but such that the direct product of M with the integers is Markov. Thus the class of Markov monoids is not closed under taking direct factors.

This is joint work with Alan Cain and Victor Maltcev.

Comments are closed.