We consider a class of algebras (defined via multiplicative commutators) which generalise
the 'canonical commutation relation'xy= λ yx of quantum mechanics. The corresponding …

Many rings that have enjoyed growing interest in recent years, eg, quantum enveloping
algebras, quantum matrices, certain Witten-algebras,…, can be presented as generalized …

Krull dimension of Generalized Weyl Algebras with non-commutative coefficients ∗ Page 1
Krull dimension of Generalized Weyl Algebras with non-commutative coefficients ∗ VV …

This paper is concerned with the Krull dimension (in the sense of Gabriel and Rentschler) of
a differential operator ring $ S [\theta;\delta] $, where $ S $ is a right noetherian ring with …

A precise formula is derived for the (noncommutative) Krull dimension of a skew-Laurent
extension R [𝜃 1±1,…, 𝜃 u±1], where R is a commutative noetherian ring of finite Krull …

Let R= A [x?',~], a skew Laurent extension of a commutative Noetherian ring A. We calculate
the Krull dimension of R (in the sense of Rentschler and Gabriel, see [2]) in the case when A …

There are many instances of skew polynomial algebras in two indeterminates x and y over
an algebra A where, for some scalar p, the" skew" commutator, xy—pyx, is in A. The most …

Behaviour of krull dimension under extension of the base field Page 1 COMMUNICATIONS IN
ALGEBRA, 19(1), 143-156 (1991) BEHAVIOUR OF KRULL DIMENSION UNDER EXTENSION …

arXiv:1106.4459v1 [math.RA] 22 Jun 2011 Page 1 arXiv:1106.4459v1 [math.RA] 22 Jun 2011
A NOTE ON THE SIMPLE MODULES OVER MCCONNELL–PETTIT ALGEBRAS ASHISH …

In this paper, a new method is developed for constructing Noetherian rings of Krull
dimension 1, and the method is used to answer some open questions concerning hereditary …