Commutatively closed rings and their graphs

Abstract: A subset S of a ring R is commutatively closed if for any elements a, b in R, the product ab is in S if and only if the product ba is in S. This concept was introduced in a recent paper and intended to have another perspective on Dedekind finite, reversible, semicommutative, ... rings. A topology was attached to this concept and in the present work we attach a graph and are able to compute the diameter of this graph for semisimple algebras. This answers some questions left open.

This is joint work with Mona Abdi.

rings and algebrasrepresentation theory

Audience: researchers in the topic

ONCAS Online Noncommutative Algebra Seminar

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