The monoid algebra of all relations on a finite set
Serge Bouc (LAMFA), Jacques Th\'evenaz (EPFL)
TL;DR
This paper classifies all simple modules of the algebra of relations on a finite set, providing their dimensions and the Jacobson radical's dimension, advancing understanding of its algebraic structure.
Contribution
It offers a complete classification of simple modules and computes key algebraic invariants for the relation algebra on finite sets, a novel structural insight.
Findings
Classified all simple modules of the algebra
Determined the dimensions of these modules
Computed the Jacobson radical's dimension
Abstract
We classify all the simple modules for the algebra of relations on a finite set, give their dimension, and find the dimension of the Jacobson radical of the algebra.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras · semigroups and automata theory