Graded monads and rings of polynomials


Models for free graded monads over the category of sets are constructed. Certain rings of generalized noncommutative polynomials, generated by an operation of arbitrary arity, are implemented as subrings of classical rings of noncommutative polynomials. It is shown that natural homomorphisms from rings of generalized polynomials to rings of the usual commutative polynomials are not inclusions as a rule. For instance, the natural homomorphism \( \mathbb{F}_{1^2 } [t] \to \mathbb{Z}[A,B], t \mapsto (A,B) \), where t is a binary variable, is not an inclusion even if t is subject to the alternating condition. Bibliography: 2 titles.

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    N. Durov, “New approach to Arakelov geometry,” arXiv: 0704.2030 v1 [math AG] 16 Apr 2007.

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    T. Leinster, “Higher operads, higher categories,” arXiv: math.CT/0305049 v1, 2 May 2003.

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Correspondence to A. L. Smirnov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 349, 2007, pp. 174–210.

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Smirnov, A.L. Graded monads and rings of polynomials. J Math Sci 151, 3032–3051 (2008).

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