Generalized Weyl Algebras Are Tensor Krull Minimal

✍ Scribed by V.V. Bavula; T.H. Lenagan

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 140 KB
• Volume: 239
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8641

✦ Synopsis

Formulae for calculating the Krull dimension of noetherian rings obtained by the authors and their collaborators are used to calculate Krull dimension for certain classes of algebras. An F-algebra T is said to be tensor Krull minimal

We show that generalized Weyl algebras over affine commutative F-algebras, where F is an uncountable algebraically closed field, are TKM with respect to the class of countably generated left noetherian F-algebras. This simplifies the task of calculating many Krull dimensions. In addition, we develop an improved formula for the Krull dimension of a skew Laurent extension w y1 x D x, x ; , where D is a polynomial algebra over an algebraically closed field, and is an affine automorphism. Finally, we calculate the Krull dimension of the noetherian down᎐up algebras introduced by Benkart.