NDLI: On topological extensions of Archimedean and non-Archimedean rings

Content Provider	Springer Nature Link
Author	Khrennikov, Andrei Yu. Walt, Jan Harm
Copyright Year	2011
Abstract	The usage of the fields of p-adic numbers Q $_{ p }$, rings of m-adic numbers Q $_{ m }$ and more general ultrametric rings in theoretical physics induced the interest to topological-algebraic studies on topological extensions of rational and real numbers and more generally (commutative and even noncommutative) rings. It is especially interesting to investigate a possibility to proceed to non-Archimedean rings by starting with real numbers. In particular, in this note we present “no-go” theorems (Theorems 3, 4) by which one cannot obtain an ultrametric ring by extending (in a natural way) the ring of real numbers. This puremathematical result has some interest for non-Archimedean physics: to explore ultrametricity one has to give up with the real numbers — to work with rings of e.g. m-adic numbers (where m > 1 is a natural, may be nonprime, number).
Starting Page	326
Ending Page	333
Page Count	8
File Format	PDF
ISSN	20700466
Journal	P-Adic Numbers, Ultrametric Analysis, and Applications
Volume Number	3
Issue Number	4
e-ISSN	20700474
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2011-11-19
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	topological extensions p-adic numbers m-adic numbers ultrametric rings non-Archimedean physics Algebra
Content Type	Text
Resource Type	Article
Subject	Mathematics

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On topological extensions of Archimedean and non-Archimedean rings