Binomial Rings: Axiomatisation, Transfer and Classification
Qimh Richey Xantcha
TL;DR
This paper provides an axiomatic foundation for binomial rings, establishes a transfer principle for combinatorial proofs, and classifies finitely generated binomial rings, with applications to modules.
Contribution
It introduces an axiomatisation of binomial rings, proves their equivalence to numerical rings, and classifies finitely generated cases, advancing the theoretical understanding of these structures.
Findings
Binomial rings are identical to numerical rings studied by Ekedahl.
The Binomial Transfer Principle enables combinatorial proofs of algebraic identities.
Finitely generated binomial rings are completely classified.
Abstract
Hall's binomial rings, rings with binomial coefficients, are given an axiomatisation and proved identical to the numerical rings studied by Ekedahl. The Binomial Transfer Principle is established, enabling combinatorial proofs of algebraical identities. The finitely generated binomial rings are completely classified. An application to modules over binomial rings is given.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra