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

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2011年 / 10卷 / 01期

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).

引用

页码：1 / 27

页数：27

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