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Zap. Nauchn. Sem. POMI, 2007, Volume 349, Pages 174–210 (Mi znsl58)  

This article is cited in 2 scientific papers (total in 2 papers)

Graded monads and rings of polynomials

A. L. Smirnov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: 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, a natural homomorphism $\mathbb{F}_{1^2}[t]\to\mathbb{Z}[A,B]$, $t\mapsto(A,B)$, where $t$ is a binary variable, isn't an inclusion, even if $t$ is subjected to the alternating condition.

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English version:
Journal of Mathematical Sciences (New York), 2008, 151:3, 3032–3051

UDC: 512.5
Received: 30.10.2007

Citation: A. L. Smirnov, “Graded monads and rings of polynomials”, Problems in the theory of representations of algebras and groups. Part 16, Zap. Nauchn. Sem. POMI, 349, POMI, St. Petersburg, 2007, 174–210; J. Math. Sci. (N. Y.), 151:3 (2008), 3032–3051

Citation in format AMSBIB
\Bibitem{Smi07}
\by A.~L.~Smirnov
\paper Graded monads and rings of polynomials
\inbook Problems in the theory of representations of algebras and groups. Part~16
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 349
\pages 174--210
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl58}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 151
\issue 3
\pages 3032--3051
\crossref{https://doi.org/10.1007/s10958-008-9013-7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-49249119277}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. L. Smirnov, “Generalized subrings of arithmetic rings”, J. Math. Sci. (N. Y.), 151:3 (2008), 3052–3068  mathnet  crossref
    2. A. L. Smirnov, “Binary projective space”, J. Math. Sci. (N. Y.), 161:4 (2009), 572–580  mathnet  crossref  zmath
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