En el marco del Coloquio del Departamento de Matemática de FIQ. Estará a cargo de George Metcalfe de la University of Bern. Joint work with Almudena Colacito, Nikolaos Galatos, and Simon Santschi.
En el marco del "Coloquio del Departamento de Matemática" de la Facultad de Ingeniería Química de la UNL, se llevará a cabo la charla:Deciding equations in ordered groups and ordered monoids. Será el 10 de noviembre a las 13hs, en idioma inglés, bajo modalidad híbrida, en el aula Babini de la FIQ y la plataforma Zoom.
- Resumen
This talk will be about deciding equations in various classes of ordered groups and ordered monoids, and how this relates to deciding if there exist orders on free groups and monoids satisfying finitely many inequalities.
Removing the inverse operation from any lattice-ordered group (l-group) yields a distributive lattice-ordered monoid (l-monoid), but not every distributive l-monoid admits a group structure. Indeed, every distributive l-monoid is a (possibly finite) pointwise-ordered monoid of order-preserving maps on a chain, whereas every l-group is a pointwise-ordered group of order-preserving permutations on a chain and is either trivial or infinite.
We will see that the equational theory of distributive l-monoids is decidable and coincides with the equational theory of l-groups without inverses, and hence, by eliminating inverses, that the equational theory of l-groups is also decidable. This contrasts with the fact that there are inverse-free equations that are satisfied by all totally ordered abelian groups but not all totally ordered commutative monoids, and the decidability of the equational theory of the latter is open.
- Short bio
George Metcalfe is a professor of mathematics at the University of Bern, Switzerland, working in the fields of universal algebra, non-classical logics, and proof theory. He completed his PhD at King's College London in the UK in 2004 and held postdoctoral positions at the Vienna University of Technology in Austria and Vanderbilt University in the US, before moving to Bern in 2009.
- Participación
La actividad es libre y gratuita. Para acceder a la reunión de Zoom es aquí, o a través de los siguientes datos:
ID de reunión: 897 5444 6861
Código de acceso: 623075