Abstract
ABSTRACT In this paper we study the behavior of the Betti numbers of a finitely generated R-module over the fiber product ring , with R, S and T being local rings with common residual field. We investigate the Buchsbaum-Eisenbud-Horrocks and Total Rank Conjectures over , and as a consequence, positive answers are given for a certain class of quotients of power series rings. A positive answer for the question posed by Jorgensen and Leuschke is also provided.
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