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Strictly analytic functions on p-adic analytic open sets.

Kamal Boussaf (1999)

Publicacions Matemàtiques

Let K be an algebraically closed complete ultrametric field. M. Krasner and P. Robba defined theories of analytic functions in K, but when K is not spherically complete both theories have the disadvantage of containing functions that may not be expanded in Taylor series in some disks. On other hand, affinoid theories are only defined in a small class of sets (union of affinoid sets) [2], [13] and [17]. Here, we suppose the field K topologically separable (example Cp). Then, we give a new definition...

Subfields of henselian valued fields

Ramneek Khassa, Sudesh K. Khanduja (2010)

Colloquium Mathematicae

Let (K,v) be a henselian valued field of arbitrary rank which is not separably closed. Let k be a subfield of K of finite codimension and v k be the valuation obtained by restricting v to k. We give some necessary and sufficient conditions for ( k , v k ) to be henselian. In particular, it is shown that if k is dense in its henselization, then ( k , v k ) is henselian. We deduce some well known results proved in this direction through other considerations.

Subgroups and hulls of Specker lattice-ordered groups

Paul F. Conrad, Michael R. Darnel (2001)

Czechoslovak Mathematical Journal

In this article, it will be shown that every ℓ -subgroup of a Specker ℓ -group has singular elements and that the class of ℓ -groups that are ℓ -subgroups of Specker ℓ -group form a torsion class. Methods of adjoining units and bases to Specker ℓ -groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker ℓ -group.

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