Proper divisibility in computable rings

DOI10.1016/J.JALGEBRA.2016.11.010zbMath1370.03021OpenAlexW2555592914MaRDI QIDQ504325

Noam Greenberg, Alexander G. Melnikov

Publication date: 16 January 2017

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2016.11.010

zbMATH Keywords

ringACAUFDreverse mathematicscomputabilityintegral domainunique factorizationACCPcomputable ringconstructive (effective) algebradivisibility relationintegral domain theory

Mathematics Subject Classification ID

Integral domains (13G05) Foundations of classical theories (including reverse mathematics) (03B30) Applications of computability and recursion theory (03D80) Second- and higher-order arithmetic and fragments (03F35) Theory of numerations, effectively presented structures (03D45) Integral domains (associative rings and algebras) (16U10)

Related Items (1)

Primitive recursive reverse mathematics

Cites Work

• Euclidean functions of computable Euclidean domains
• Recursive properties of Euclidean domains
• Countable algebra and set existence axioms
• AP-domains and unique factorization.
• Computable structures and the hyperarithmetical hierarchy
• Ideals in computable rings
• Iterated effective embeddings of abelian p-groups
• Chain conditions in computable rings
• Effective procedures in field theory
• Effective content of field theory
• Recursively enumerable vector spaces
• Jump degrees of torsion-free abelian groups
• CONSTRUCTIVE ALGEBRAS I
• Computable Algebra, General Theory and Theory of Computable Fields
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