Open AccessAlgebraic properties of external numbers
Author(s) -
Bruno Dinis,
Imme van den Berg
Publication year - 2011
Publication title -
journal of logic and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.278
H-Index - 4
ISSN - 1759-9008
DOI - 10.4115/jla.2011.3.9
Subject(s) - mathematics , algebraic number , pure mathematics , algebra over a field , combinatorics , mathematical analysis
Neutrices and external numbers were proposed as models of orders of magnitude within nonstandard analysis. We show that the external numbers form a commutative regular semigroup for addition and that the external numbers which are not neutrices form a commutative regular semigroup for multiplication. The validity of the distributive law is restricted, but it can be fully characterized. 2000 Mathematics Subject Classification 03H05 (primary); 06F05, 20M14, 20M17 (secondary)
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