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Algebra Logika, 2019, Volume 58, Number 6, Pages 741–768 (Mi al927)  

A correspondence between commutative rings and Jordan loops

V. I. Ursuab

a Technical University of Moldova
b Institute of Mathematics "Simion Stoilow" of the Romanian Academy

Abstract: We show that there is a one-to-one correspondence (up to isomorphism) between commutative rings with unity and metabelian commutative loops belonging to a particular finitely axiomatizable class. Based on this correspondence, it is proved that the sets of identically valid formulas and of finitely refutable formulas of a class of finite nonassociative commutative loops (and of many of its other subclasses) are recursively inseparable. It is also stated that nonassociative commutative free automorphic loops of any nilpotency class have an undecidable elementary theory.

Keywords: commutative ring with unity, metabelian commutative loop, finitely axiomatizable class, undecidability of elementary theory, recursively inseparable sets.

DOI: https://doi.org/10.33048/alglog.2019.58.605

Full text: PDF file (272 kB)
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English version:
Algebra and Logic, 2020, 58:6, 494–513

Bibliographic databases:

UDC: 512.548.77+512.572
Received: 23.06.2017
Revised: 12.02.2020

Citation: V. I. Ursu, “A correspondence between commutative rings and Jordan loops”, Algebra Logika, 58:6 (2019), 741–768; Algebra and Logic, 58:6 (2020), 494–513

Citation in format AMSBIB
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\by V.~I.~Ursu
\paper A correspondence between commutative rings and Jordan loops
\jour Algebra Logika
\yr 2019
\vol 58
\issue 6
\pages 741--768
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\crossref{https://doi.org/10.33048/alglog.2019.58.605}
\transl
\jour Algebra and Logic
\yr 2020
\vol 58
\issue 6
\pages 494--513
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