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Crossed Product Orders over Valuation Rings
Author(s) -
Kauta John S.
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609301008359
Subject(s) - mathematics , krull dimension , crossed product , discrete valuation , quotient , valuation (finance) , valuation ring , pure mathematics , brauer group , order (exchange) , discrete mathematics , combinatorics , algebra over a field , field (mathematics) , noetherian , finance , economics
Let V be a commutative valuation domain of arbitrary Krull‐dimension (rank), with quotient field F , and let K be a finite Galois extension of F with group G , and S the integral closure of V in K . If, in the crossed product algebra K * G , the 2‐cocycle takes values in the group of units of S , then one can form, in a natural way, a ‘crossed product order’ S * G ⊆ K * G . In the light of recent results by H. Marubayashi and Z. Yi on the homological dimension of crossed products, this paper discusses necessary and/or sufficient valuation‐theoretic conditions, on the extension K / F , for the V ‐order S * G to be semihereditary, maximal or Azumaya over V . 2000 Mathematics Subject Classification 16H05, 16S35.