On Rayner structures
In this note, we study substructures of generalized power series fields induced by families of
well-ordered subsets of the group of exponents. We characterize the set-theoretic and …
well-ordered subsets of the group of exponents. We characterize the set-theoretic and …
Quasi-valuations extending a valuation
S Sarussi - Journal of Algebra, 2012 - Elsevier
Suppose F is a field with valuation v and valuation ring Ov, E is a finite field extension and w
is a quasi-valuation on E extending v. We study quasi-valuations on E that extend v; in …
is a quasi-valuation on E extending v. We study quasi-valuations on E that extend v; in …
Real closed exponential fields
P D'Aquino, JF Knight, S Kuhlmann… - arXiv preprint arXiv …, 2011 - arxiv.org
In an extended abstract Ressayre considered real closed exponential fields and integer
parts that respect the exponential function. He outlined a proof that every real closed …
parts that respect the exponential function. He outlined a proof that every real closed …
Hardy type derivations on fields of exponential logarithmic series
S Kuhlmann, M Matusinski - Journal of Algebra, 2011 - Elsevier
We consider the valued field K:= R ((Γ)) of formal series (with real coefficients and
monomials in a totally ordered multiplicative group Γ). We investigate how to endow K with a …
monomials in a totally ordered multiplicative group Γ). We investigate how to endow K with a …
Selected methods for the classification of cuts, and their applications
FV Kuhlmann - arXiv preprint arXiv:1803.07806, 2018 - arxiv.org
arXiv:1803.07806v1 [math.AC] 21 Mar 2018 Page 1 arXiv:1803.07806v1 [math.AC] 21 Mar
2018 SELECTED METHODS FOR THE CLASSIFICATION OF CUTS, AND THEIR …
2018 SELECTED METHODS FOR THE CLASSIFICATION OF CUTS, AND THEIR …
Totally ordered sets and the prime spectra of rings
S Sarussi - Communications in Algebra, 2017 - Taylor & Francis
Let T be a totally ordered set and let D (T) denotes the set of all cuts of T. We prove the
existence of a discrete valuation domain O v such that T is order isomorphic to two special …
existence of a discrete valuation domain O v such that T is order isomorphic to two special …
Quasi-valuations and algebras over valuation domains
S Sarussi - Communications in Algebra, 2019 - Taylor & Francis
Suppose F is a field with valuation v and valuation domain Ov, and R is an Ov-algebra. We
prove that R satisfies SGB (strong going between) over Ov. We give a necessary and …
prove that R satisfies SGB (strong going between) over Ov. We give a necessary and …
Mini-workshop: Surreal numbers, surreal analysis, Hahn fields and derivations
A Berarducci, P Ehrlich, S Kuhlmann - Oberwolfach Reports, 2017 - ems.press
New striking analogies between H. Hahn's fields of generalised series with real coefficients,
GH Hardy's field of germs of real valued functions, and JH Conway's field No of surreal …
GH Hardy's field of germs of real valued functions, and JH Conway's field No of surreal …
Arithmetic of cuts in ordered abelian groups and of ideals over valuation rings
FV Kuhlmann - arXiv preprint arXiv:2406.10545, 2024 - arxiv.org
We investigate existence, uniqueness and maximality of solutions $ T $ for equations $
S_1+ T= S_2 $ and inequalities $ S_1+ T\subseteq S_2 $ where $ S_1 $ and $ S_2 $ are …
S_1+ T= S_2 $ and inequalities $ S_1+ T\subseteq S_2 $ where $ S_1 $ and $ S_2 $ are …
Extensions of integral domains and quasi-valuations
S Sarussi - Communications in Algebra, 2020 - Taylor & Francis
Let S be an integral domain with field of fractions F and let A be an F-algebra having an S-
stable basis. We prove the existence of an S-subalgebra R of A lying over S whose …
stable basis. We prove the existence of an S-subalgebra R of A lying over S whose …