Structure of prime finitely presented monomial algebras

JOURNAL OF ALGEBRA

卷:320

Article

Okninski, Jan

关键词: monomial algebra;    finitely presented;    primitive algebra;    semigroup algebra;   

DOI  :  10.1016/j.jalgebra.2008.08.003

来源: Elsevier

【 摘 要 】

The structure of a finitely presented monomial algebra K[X]/K[l] over a field K is described. Here X is a finitely generated free monoid and I is a prime ideal of X that is finitely generated. As an application, a new structural proof of the recent result of Bell and Pekcagliyan [J. Bell, P. Pekcagliyan, Primitivity of finitely presented monomial algebras. preprint, arXiv: 0712.0815v1] on the primitivity of such algebras is presented, which yields a positive solution to the trichotomy problem. raised by Bell and Smoktunowicz [J. Bell, A. Smoktunowicz. The prime spectrum of algebras of quadratic growth, J. Algebra 319 (2008) 414-431], in the finitely presented case. Our approach is based on a new result on the form of prime Rees factors of semigroups satisfying the ascending chain condition on one-sided annihilators and on its refinement in the case of finitely presented factors of the form X/l. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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