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ON THE CONNECTION BETWEEN DIFFERENTIAL POLYNOMIAL RINGS AND POLYNOMIAL RINGS OVER NIL RINGS

  • LOUISA CATALANO (a1) and MEGAN CHANG-LEE (a2)

Abstract

In this paper, we study some connections between the polynomial ring $R[y]$ and the differential polynomial ring $R[x;D]$ . In particular, we answer a question posed by Smoktunowicz, which asks whether $R[y]$ is nil when $R[x;D]$ is nil, provided that $R$ is an algebra over a field of positive characteristic and $D$ is a locally nilpotent derivation.

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The authors are supported in part by NSF grant DMS 1653002.

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[1] Amitsur, S. A., ‘Radicals of polynomial rings’, Canad. J. Math. 8 (1956), 355361.
[2] Smoktunowicz, A., ‘Polynomial rings over nil rings need not be nil’, J. Algebra 233 (2000), 427436.
[3] Smoktunowicz, A., ‘How far can we go with Amitsur’s theorem in differential polynomial rings?’, Israel J. Math. 219 (2017), 555608.
[4] Smoktunowicz, A. and Ziembowski, M., ‘Differential polynomial rings over locally nilpotent rings need not be Jacobson radical’, J. Algebra 412 (2014), 207217.
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ON THE CONNECTION BETWEEN DIFFERENTIAL POLYNOMIAL RINGS AND POLYNOMIAL RINGS OVER NIL RINGS

  • LOUISA CATALANO (a1) and MEGAN CHANG-LEE (a2)

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