Rationals with exotic convergences. II.
Real holomorphy rings and the complete real spectrum
The complete real spectrum of a commutative ring with is introduced. Points of the complete real spectrum are triples , where is a real prime of , is a real valuation of the field and is an ordering of the residue field of . is shown to have the structure of a spectral space in the sense of Hochster [5]. The specialization relation on is considered. Special attention is paid to the case where the ring in question is a real holomorphy ring.
Real spectra of complete local rings.
Reine lokale Ringe der Dimension zwei.
Relations between localizations and -adic completions in commutative domains
Relatively complete ordered fields without integer parts
We prove a convenient equivalent criterion for monotone completeness of ordered fields of generalized power series with exponents in a totally ordered Abelian group G and coefficients in an ordered field F. This enables us to provide examples of such fields (monotone complete or otherwise) with or without integer parts, i.e. discrete subrings approximating each element within 1. We include a new and more straightforward proof that is always Scott complete. In contrast, the Puiseux series field...
Remarks on Banach- -algebras. (Remarques sur les -algèbres de Banach.)
Remarks on the elementary theories of formal and convergent power series
Remarks on the Lifting of Algebras over Henselian Pairs.
Representations of non-negative polynomials having finitely many zeros
Consider a compact subset of real -space defined by polynomial inequalities . For a polynomial non-negative on , natural sufficient conditions are given (in terms of first and second derivatives at the zeros of in ) for to have a presentation of the form , a sum of squares of polynomials. The conditions are much less restrictive than the conditions given by Scheiderer in [11, Cor. 2.6]. The proof uses Scheiderer’s main theorem in [11] as well as arguments from quadratic form theory...
Résultats récents sur l'approximation des morphismes en algèbre commutative
Rings in Which Pure Ideals are Generated by Idempotents.
Rings with approximation property.
Ringtopologien auf Z und Q.
Rückert Nullstellensatz for normed, non-discrete fields using non-standard analysis.