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A note on the Krull dimension of certain algebras
Author(s) -
Wehrfritz B. A. F.
Publication year - 1992
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300006835
Subject(s) - mathematics , krull dimension , dimension (graph theory) , polynomial ring , mathematical proof , skew , ring (chemistry) , pure mathematics , field (mathematics) , algebra over a field , polynomial , discrete mathematics , noetherian , mathematical analysis , astronomy , chemistry , physics , geometry , organic chemistry
. For F a field we compute, explicitly and directly, the right Krull dimension of the algebra Q op ⊗ F Q 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.