文档介绍：DIVISOR THEORY IN MODULE CATEGORIES
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NORTH-HOLLAND
MATHEMATICS STUDIES 14
Notas de Matematica (53)
Editor: Leopoldo Nachbin
Universidade Federaldo Rio de Jarmiro
and University of Rochester
Divisor Theory in Module
Cat ego ries
W. V. VASCONCELOS
Rutgers University
1974
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Preface
Heuristically the divisor -d(E) of an A-module E is the
ideal of A nackiny the most information on E. A nrime candidate
for this role, the annihilator of E, lacks decent functorial
properties. Instead, a generalization of another of the classi -
cal divisors nlays a more visible role if one works in the
following setting. Define a divisor on a suhcateyory C of
mod(R) as an additive - with resnect to short exact sequences -
mapping from C into some semi-groun S of ideals. An outstandinp
example is that found in the category T of finitely generated
torsion modules of finite projective dimension over a Nocther -
ian ring A. In this case one may define a divisor function from
T into the semi-group Inv(A) of invertible ideals and obtain an
exact sequence
- A -d
Ko(A)- Ko(T)- Inv(A) - 1.
This -d is def