Bass numbers and semidualizing complexes
S Sather-Wagstaff - Commutative algebra and its applications, 2009 - degruyter.com
Commutative algebra and its applications, 2009•degruyter.com
Let R be a commutative local Noetherian ring. We prove that the existence of a chain of
semidualizing R-complexes of length. d C 1/yields a degree-d polynomial lower bound for
the Bass numbers of R. We also show how information about certain Bass numbers of R
provides restrictions on the lengths of chains of semidualizing R-complexes. To make this
article somewhat self-contained, we also include a survey of some of the basic properties of
semidualizing modules, semidualizing complexes and derived categories.
semidualizing R-complexes of length. d C 1/yields a degree-d polynomial lower bound for
the Bass numbers of R. We also show how information about certain Bass numbers of R
provides restrictions on the lengths of chains of semidualizing R-complexes. To make this
article somewhat self-contained, we also include a survey of some of the basic properties of
semidualizing modules, semidualizing complexes and derived categories.
Abstract
Let R be a commutative local Noetherian ring. We prove that the existence of a chain of semidualizing R-complexes of length. d C 1/yields a degree-d polynomial lower bound for the Bass numbers of R. We also show how information about certain Bass numbers of R provides restrictions on the lengths of chains of semidualizing R-complexes. To make this article somewhat self-contained, we also include a survey of some of the basic properties of semidualizing modules, semidualizing complexes and derived categories.
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