Elementary arithmetic as inverse semigroup theory

Abstract: This talk considers some very elementary arithmetic operations from the viewpoint of inverse semigroup theory, category theory, and the theory of Cantor spaces. It starts by deriving monotone partial injections -- hence inverse semigroups -- from basic arithmetic operations, and goes on to interpret these as simple examples of well-known categorical properties and structures. This leads in a natural way to several very well-known inverse monoids, and strict generalisations of these. These generalisations have a close connection to elementary number-theory, computability, and formal undecidability.

category theorygroup theoryrings and algebras

Audience: researchers in the topic

York semigroup seminar

Series comments: Description: Semigroup-related research talks at University of York.

Email Nora Szakacs at nora.szakacs@york.ac.uk for the meeting password.