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A completion of is a field

José E. Marcos (2003)

Czechoslovak Mathematical Journal

We define various ring sequential convergences on and . We describe their properties and properties of their convergence completions. In particular, we define a convergence 𝕃 1 on by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields / ( p ) . Further, we show that ( , 𝕃 1 * ) is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.

Adic-completion and some dual homological results.

Anne-Marie Simon (1992)

Publicacions Matemàtiques

Let a be an ideal of a commutative ring A. There is a kind of duality between the left derived functors Uia of the a-adic completion functor, called local homology functors, and the local cohomology functors Hai.Some dual results are obtained for these Uia, and also inequalities involving both local homology and local cohomology when the ring A is noetherian or more generally when the Ua and Ha-global dimensions of A are finite.

Formal prime ideals of infinite value and their algebraic resolution

Steven Dale Cutkosky, Samar ElHitti (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Suppose that R is a local domain essentially of finite type over a field of characteristic 0 , and ν a valuation of the quotient field of R which dominates R . The rank of such a valuation often increases upon extending the valuation to a valuation dominating R ^ , the completion of R . When the rank of ν is 1 , Cutkosky and Ghezzi handle this phenomenon by resolving the prime ideal of infinite value, but give an example showing that when the rank is greater than 1 , there is no natural ideal in R ^ that...

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