2002/10/15 by T. Gateva-Ivanova, Gateva-Ivanova, T., Eric Jespers +3
Mathematics · #16P40 #16S15 #16S36 #20M25 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16P40 #msc:16S15 #msc:16S36 #msc:20M25
paper · pdf · doi:10.48550/arxiv.math/0210217
Work supported in part by Onderzoeksraad of Vrije Universiteit Brussel, Fonds voor Wetenschappelijk Onderzoek (Belgium), and KBN research grant 2P03A 030 18 (Poland)
arxiv created 2002/10/15 · arxiv updated 2009/11/30
We consider algebras over a field K defined by a presentation K <x1,..., xn : R >, where R consists of n choose 2 square-free relations of the form xi xj = xk xl with every monomial xi xj, i different from j, appearing in one of the relations. Certain sufficient conditions for the algebra to be noetherian and PI are determined. For this, we prove more generally that right noetherian algebras of finite Gelfand-Kirillov dimension defined by homogeneous relations satisfy a polynomial identity. The structure of the underlying monoid, defined by the same presentation, is described. This is used to derive information on the prime radical and minimal prime ideals. Some examples are described in detail. Earlier, Etingof, Schedler and Soloviev, Gateva-Ivanova and Van den Bergh, and the authors considered special classes of such algebras in the contexts of noetherian algebras, Grobner bases, finitely generated solvable groups, semigroup algebras, and set theoretic solutions of the Yang-Baxter equation.