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Primary differential nil-algebras do exist

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Abstract

We construct a monomorphism from the differential algebra k{x}/[x m] to a Grassmann algebra endowed with a structure of differential algebra. Using this monomorphism, we prove the primality of k{x}/[x m] and its algebra of differential polynomials, solve one of so-called Ritt problems related to this algebra, and give a new proof of the integrality of ideal [x m].

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    G. A. Pogudin

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  1. G. A. Pogudin
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Original Russian Text © G.A. Pogudin, 2014, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2014, Vol. 69, No. 1, pp. 50–53.

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Pogudin, G.A. Primary differential nil-algebras do exist. Moscow Univ. Math. Bull. 69, 33–36 (2014). https://doi.org/10.3103/S0027132214010069

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  • DOI: https://doi.org/10.3103/S0027132214010069

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