The algebra of essential relations on a finite set
2013
Online
report
Let 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 the Jacobson radical and of all the simple modules for the essential algebra.
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The algebra of essential relations on a finite set
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Autor/in / Beteiligte Person: | Bouc, Serge ; Thévenaz, Jacques |
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Veröffentlichung: | 2013 |
Medientyp: | report |
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