Vol. 35, No. 2, 1970

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Generic splitting algebras for Pic

Gerald Seymour Garfinkel

Vol. 35 (1970), No. 2, 369–380

Our purpose is to develop a splitting theory for the functor Pic. For each rank one projective module P, we exhibit a generic splitting algebra T(P∕R). Whenever n is a multiple of the order of P in Pic (R), it has a splitting algebra which is a rank n projective module. We then show the relationship of the latter algebra to the usual splitting ring of an ideal in a Dedekind domain.

Mathematical Subject Classification
Primary: 13.90
Received: 10 March 1970
Published: 1 November 1970
Gerald Seymour Garfinkel