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On Semihereditary Maximal Orders
Author(s) -
Kauta John S.
Publication year - 1998
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/s0024609397004049
Subject(s) - mathematics , order (exchange) , maximal ideal , combinatorics , intersection (aeronautics) , ideal (ethics) , mathematics subject classification , law , engineering , finance , political science , economics , aerospace engineering
Let A be an order integral over a valuation ring V in a central simple F ‐algebra, where F is the fraction field of V . We show that (a) if ( V h , F h ) is the Henselization of ( V , F ), then A is a semihereditary maximal order if and only if A ⊗ V V h is a semihereditary maximal order, generalizing the result by Haile, Morandi and Wadsworth, and (b) if J ( V ) is a principal ideal of V , then a semihereditary V ‐order is an intersection of finitely many conjugate semihereditary maximal orders; if not, then there is only one maximal order containing the V ‐order. 1991 Mathematics Subject Classification 16H05.