Binomial Rings: Axiomatisation, Transfer and Classification

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Xantcha, Qimh Richey (2011)
  • Subject: Mathematics - Rings and Algebras | 13F99 (Primary), 13F20 (Secondary) | Mathematics - Commutative Algebra
    arxiv: Mathematics::Commutative Algebra

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.
  • References (11)
    11 references, page 1 of 2

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    [3] Jesse Elliott: Binomial rings, integer-valued polynomials, and l-rings, Journal of Pure and Applied Algebra 207, 2006.

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    [5] Philip Hall: The Edmonton Notes on Nilpotent Groups, Queen Mary College Mathematics Notes 1976.

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    [7] Clarence Wilkerson: Lambda-Rings, Binomial Domains, and Vector Bundles over CPp8q, Communications in Algebra 10 (3), 1982.

    [8] Qimh Xantcha: The Theory of Polynomial Functors, doctoral dissertation, Stockholm University 2010.

    [9] Qimh Richey Xantcha: Polynomial Maps of Modules, submitted.

    [10] Qimh Richey Xantcha: Polynomial Functors of Modules, submitted.

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