Structure of Chinese algebras
Copyright policy )Structure of Chinese algebras
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.
- Vrije Universiteit Brussel Belgium
- University of Warsaw Poland
- Institute of Mathematics Poland
- Polish Academy of Sciences Poland
- Warsaw University of Technology Poland
Prime and semiprime associative rings, Free semigroups, generators and relations, word problems, Prime ideal, Monoid algebra, FOS: Mathematics, Radical, 16S15 (Primary), 16S36, 16N60, 20M05, 20M25 (Secondary), Representation Theory (math.RT), Homogeneous congruence, Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting), monoid algebras, homogeneous congruences, Algebra and Number Theory, Chinese monoids, presentations, Chinese monoid, Chinese algebra, Semigroup rings, multiplicative semigroups of rings, representations, prime ideals, Mathematics - Rings and Algebras, radicals, Ordinary and skew polynomial rings and semigroup rings, Rings and Algebras (math.RA), Ideals in associative algebras, Mathematics - Representation Theory
Prime and semiprime associative rings, Free semigroups, generators and relations, word problems, Prime ideal, Monoid algebra, FOS: Mathematics, Radical, 16S15 (Primary), 16S36, 16N60, 20M05, 20M25 (Secondary), Representation Theory (math.RT), Homogeneous congruence, Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting), monoid algebras, homogeneous congruences, Algebra and Number Theory, Chinese monoids, presentations, Chinese monoid, Chinese algebra, Semigroup rings, multiplicative semigroups of rings, representations, prime ideals, Mathematics - Rings and Algebras, radicals, Ordinary and skew polynomial rings and semigroup rings, Rings and Algebras (math.RA), Ideals in associative algebras, Mathematics - Representation Theory
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).12 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!