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[11]
Halter-Koch F., 1998, Ideal Systems: An Introduction to Multiplicative Ideal Theory
MAXIMAL IDEALS IN PREADDITIVE CATEGORIES AND SEMILOCAL CATEGORIES
被引：10
作者：
Facchini, Alberto
[1
]
Perone, Marco
[1
]
机构：
[1] Univ Padua, Dipartimento Matemat Pura & Applicata, I-35121 Padua, Italy
关键词：
Maximal ideal;
preadditive category;
additive category;
simple category;
trace ideal;
Morita equivalence;
DIRECT-SUM DECOMPOSITIONS;
ENDOMORPHISM-RINGS;
MODULES;
D O I：
10.1142/S0219498811004458
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The first aim of this article is to study maximal ideals of a preadditive category C. Maximal ideals, which do not exist in general for arbitrary preadditive categories, are associated to a maximal ideal of the endomorphism ring of an object and always exist when the category is semilocal. If C is additive and semilocal, any skeleton V(C) of C is a Krull monoid and we are able to characterize the essential valuations of V(C) and provide some natural divisor homomorphisms and divisor theories of V(C).
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页码：1 / 27
页数：27
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