Bouc, SergeThévenaz, Jacques2013-12-202013-12-202013-12-20201610.1515/crelle-2014-0019https://infoscience.epfl.ch/handle/20.500.14299/98621WOS:000371097200010Let X be a finite set and let k be a commutative ring. We consider the k-algebra of the monoid of all relations on X, modulo the ideal generated by the relations factorizing through a set of cardinality strictly smaller than Card(X), called inessential relations. This quotient is called the essential algebra associated to X. We then define a suitable nilpotent ideal of the essential algebra and describe completely the structure of the corresponding quotient, a product of matrix algebras over suitable group algebras. In particular, we obtain a description of all the simple modules for the essential algebra.text::journal::journal article::research article