 
Summary: TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 335, Number 2, February 1993
BASS SERIES OF LOCAL RING HOMOMORPHISMS
OF FINITE FLAT DIMENSION
LUCHEZAR L. AVRAMOV, HANSBJØRN FOXBY, AND JACK LESCOT
Dedicated to Robert Fossum on his fiftieth birthday
Abstract. Nontrivial relations between Bass numbers of local commu
tative rings are established in case there exists a local homomorphism
OE: R ! S which makes S into an Rmodule of finite flat dimension.
In particular, it is shown that an inequality ¯ i+depth R
R ¯ i+depth S
s
holds for all i 2 Z. This is a consequence of an equality involving
the Bass series I M
R (t) = P
i2Z ¯ i
R (M)t i of a complex M of Rmodules
which has bounded above and finite type homology and the Bass series of
the complex of Smodules
