Prüfer ⋆–multiplication domains and ⋆–coherence

A "υ-Operation Free" Approach to Prüfer υ-Multiplication Domains

The so-called Prüfer υ-multiplication domains PυMDs are usually defined as domains whose finitely generated nonzero ideals are t-invertible. These domains generalize Prüfer domains and Krull domains. The PυMDs are relatively obscure compared to their verywell-known special cases. One of the reasons could be that the study of PυMDs uses the jargon of star operations, such as the υ-operation and ...

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Note on Colon-Multiplication Domains

Coherence of Associativity in Categories with Multiplication

To say that C is a category with (functoral) multiplication means that there is a functor ⊗ : C → C called the multiplication where C is the category of pairs of objects and pairs of morphisms from C. [More technically, C is the category of functors and natural transformations from 2 to C where 2 is the category with objects 0 and 1, and the only morphisms are the identity morphisms.] Examples ...

Curves and coherent Prüfer rings

Usual definitions of Dedekind domain are not well suited for an algorithmic treatment. Indeed, the notion of Noetherian rings is subtle from a constructive point of view, and to be able to get prime ideals involve strong hypotheses. For instance, if k is a field, even given explicitely, there is in general no method to factorize polynomials in k[X]. The work [2] analyses the notion of Dedekind ...