Vol. 74, No. 2, 1978

Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Hereditary crossed product orders

Héctor Alfredo Merklen

Vol. 74 (1978), No. 2, 391–406

In this paper one deals with crossed product orders Λ of the following form: Let be a Dedekind domain with quotient field and a semisimple, commutative, algebra of finite dimension over . Let 𝒢 be a finite subgroup of the group of automorphisms of whose fixed subalgebra is , and let Λ0 be an -order in , which is 𝒢-stable. Then, if [f] is an element of the second cohomology group H2(𝒢,U0)), our order is Λ = Δ(f,Λ0,𝒢). One is interested in the set of all maximal orders in 𝒜 = Δ(f,,𝒢) which contain Λ and also in all hereditary orders in 𝒜 which contain Λ. In particular, one is interested in knowing sufficient conditions for Λ itself to be hereditary. This last question is answered by Theorem 1, and the other, more general question, is succesively reduced to the classical complete case (i.e., when is a local complete Dedekind domain and is a Galois field extension of with group 𝒢), to the totally ramified case (i.e., when, furthermore, is totally ramified) and, finally, to the wildly ramified case.

Mathematical Subject Classification
Primary: 16A14, 16A14
Secondary: 16A18
Received: 1 November 1973
Revised: 6 May 1975
Published: 1 February 1978
Héctor Alfredo Merklen