Skew Polynomial Rings with Binomial Relations

✍ Scribed by Tatiana Gateva-Ivanova

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 343 KB
• Volume: 185
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.0348

✦ Synopsis

In this paper we continue the study of a class of standard finitely presented quadratic algebras A over a fixed field K, called binomial skew polynomial rings. We consider some combinatorial properties of the set of defining relations F and their implications for the algebraic properties of A. We impose a condition, called Ž .

) , on F and prove that in this case A is a free module of finite rank over a strictly ordered Noetherian domain. We show that an analogue of the Diamond Ž . Lemma is true for one-sided ideals of a skew polynomial ring A with condition ) . We prove, also, that if the set of defining relations F is square free, then condition Ž .

) is necessary and sufficient for the existence of a finite Groebner basis of every one-sided ideal in A, and for left and right Noetherianness of A. As a corollary we find a class of finitely generated non-commutative semigroups which are left and right Noetherian.