Tensor homological minimal algebras, global dimension of the tensor product of algebras and of generalized Weyl algebras
type: Item
instance of: scholarly article
title: Tensor homological minimal algebras, global dimension of the tensor product of algebras and of generalized Weyl algebras
zbMATH Open document ID: 0855.16010
published in: Bulletin des Sciences Mathématiques
publication date: 1997-01-27T00:00:00Z
review text: An algebra \(A\) over a field is called tensor-\(d\)-minimal with respect to some class of algebras \(\Omega\), if \(d(A\otimes B)=d(A)+d(B)\) for each \(B\in\Omega\) where \(d\) is one of the following dimensions of rings: the weak dimension (wd), the left homological dimension (lgd), the Krull dimension (kd). The author gives sufficient conditions for an algebra to be tensor \(d\)-minimal. In particular, it is proved that the Weyl algebra \(A_n\) over an algebraically closed uncountable field is tensor lgd-minimal with respect to the class of all finitely generated left Noetherian algebras. It should be noted also that the author computes the global dimension of the generalized Weyl algebra of degree one with basic Dedekind ring.
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16S32
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16P90
zbMATH DE Number: 915280
zbMATH Keywords: tensor minimal algebras
zbMATH Keywords: weak dimension
zbMATH Keywords: left homological dimension
zbMATH Keywords: Krull dimension
zbMATH Keywords: Weyl algebras
zbMATH Keywords: finitely generated left Noetherian algebras
zbMATH Keywords: global dimension
zbMATH Keywords: generalized Weyl algebras
author: V. V. Bavula
reviewed by: Yu. N. Maltsev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 915280