×

A note on the Krull dimension of certain algebras. (English) Zbl 0738.16004

For \(F\) a field we compute, explicitly and directly, the right Krull dimension of the algebra \(Q^{op}\otimes_ FQ\) for certain semisimple Artinian \(F\)-algebras \(Q\). (Here \(Q^{op}\) denotes the opposite ring of \(Q\).) We use our calculation to give alternative proofs of some theorems of J. T. Stafford and A. I. Lichtman. Our methods involve a detailed study of skew polynomial rings.

MSC:

16K20 Finite-dimensional division rings
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16S36 Ordinary and skew polynomial rings and semigroup rings
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1007/BF02764919 · Zbl 0404.16012 · doi:10.1007/BF02764919
[2] McConnell, Non-commutative Noetherian Rings (1987)
[3] DOI: 10.1007/BF02760668 · Zbl 0517.16014 · doi:10.1007/BF02760668
[4] DOI: 10.1080/00927878508823250 · Zbl 0567.16002 · doi:10.1080/00927878508823250
[5] Shirvani, Skew Linear Groups (1986) · Zbl 0602.20046
[6] Chatters, Rings with Chain Conditions (1980)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.