Structure of Chinese algebras

Details Structure of Chinese algebras Structure of Chinese algebras

2010-09-29

arxiv.org/abs/1009.5847v2

Mathematics

Rings and Algebras

Scientific paper

The structure of the algebra K[M] of the Chinese monoid M over a field K is studied. The minimal prime ideals are described. They are determined by certain homogeneous congruences on M and they are in a one to one correspondence with diagrams of certain special type. There are finitely many such ideals. It is also shown that the prime radical B(K[M]) of K[M] coincides with the Jacobson radical and the monoid M embeds into the algebra K[M]/B(K[M]). A new representation of M as a submonoid of the direct product of finitely many copies of the bicyclic monoid and finitely many copies of the infinite cyclic monoid is derived. Consequently, M satisfies a nontrivial identity.

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