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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Universiteit van Ams...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
https://doi.org/10.1007/978-3-...
Part of book or chapter of book . 2008 . Peer-reviewed
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Fields, Meadows and Abstract Data Types

Authors: Bergstra, J.; Hirschfeld, Y.; Tucker, J.;

Fields, Meadows and Abstract Data Types

Abstract

Fields and division rings are not algebras in the sense of "Universal Algebra", as inverse is not a total function. Mending the inverse by any definition of 0(-1) will not suffice to axiomatize the axiom of inverse x(-1) · x = 1, by an equation. In particular the theory of fields cannot be used for specifying the abstract data type of the rational numbers.We define equational theories of Meadows and of Skew Meadows, and we prove that these theories axiomatize the equational properties of fields and of division rings, respectively, with 0(-1) = 0. Meadows are then used in the theory of Von Neumann regular ring rings to characterize strongly regular rings as those that support an inverse operation that turns it into a skew meadow. To conclude, we present in this framework the specification of the abstract type of the rational numbers, as developed by the first and third authors in [2].

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Netherlands
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004, 510

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Average
Top 10%
Average
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