natural divisor
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2011 ◽  
Vol 10 (01) ◽  
pp. 1-27 ◽  
Author(s):  
ALBERTO FACCHINI ◽  
MARCO PERONE

The first aim of this article is to study maximal ideals of a preadditive category [Formula: see text]. 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 [Formula: see text] is additive and semilocal, any skeleton [Formula: see text] of [Formula: see text] is a Krull monoid and we are able to characterize the essential valuations of [Formula: see text] and provide some natural divisor homomorphisms and divisor theories of [Formula: see text].


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