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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
 

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 Ÿ ¯ 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

  

Source: Avramov, Luchezar L.- Department of Mathematics, University of Nebraska-Lincoln

 

Collections: Mathematics