scholarly journals On differential polynomial rings over locally nilpotent rings

2018 ◽  
Vol 227 (1) ◽  
pp. 233-238 ◽  
Author(s):  
Mikhail Chebotar
Keyword(s):  
Differential Polynomial ◽  
Polynomial Rings ◽  
Locally Nilpotent

Differential polynomial rings in several variables over locally nilpotent rings

2019 ◽  
Vol 30 (01) ◽  
pp. 117-123 ◽  
Author(s):  
Fei Yu Chen ◽  
Hannah Hagan ◽  
Allison Wang
Keyword(s):  
Polynomial Ring ◽  
Differential Polynomial ◽  
Polynomial Rings ◽  
Nilpotent Ring ◽  
Several Variables ◽  
Locally Nilpotent ◽  
Differential Polynomial Ring

We show that a differential polynomial ring over a locally nilpotent ring in several commuting variables is Behrens radical, extending a result by Chebotar.

Derivations and bounded nilpotence index

2015 ◽  
Vol 25 (03) ◽  
pp. 433-438 ◽  
Author(s):  
Pace P. Nielsen ◽  
Michał Ziembowski
Keyword(s):  
Polynomial Ring ◽  
Differential Polynomial ◽  
Prime Radical ◽  
Polynomial Rings ◽  
Locally Nilpotent ◽  
Differential Polynomial Ring ◽  
Index Of Nilpotence ◽  
Nil Ring ◽  
Strong Barrier

We construct a nil ring R which has bounded index of nilpotence 2, is Wedderburn radical, and is commutative, and which also has a derivation δ for which the differential polynomial ring R[x;δ] is not even prime radical. This example gives a strong barrier to lifting certain radical properties from rings to differential polynomial rings. It also demarcates the strength of recent results about locally nilpotent PI rings.

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

2019 ◽  
Vol 101 (3) ◽  
pp. 438-441
Author(s):  
LOUISA CATALANO ◽  
MEGAN CHANG-LEE
Keyword(s):  
Polynomial Ring ◽  
Positive Characteristic ◽  
Differential Polynomial ◽  
Polynomial Rings ◽  
Locally Nilpotent Derivation ◽  
Locally Nilpotent ◽  
Nilpotent Derivation ◽  
Differential Polynomial Ring ◽  
Field Of Positive Characteristic ◽  
Algebra Over A Field

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.

Radicals in differential polynomial rings

2020 ◽  
pp. 1-17
Author(s):  
Jongwook Baeck ◽  
Nam Kyun Kim ◽  
Yang Lee
Keyword(s):  
Differential Polynomial ◽  
Prime Radical ◽  
Polynomial Rings

In this paper, we present new characterizations of several radicals of differential polynomial rings, including the Levitzki radical, strongly prime radical, and uniformly strongly prime radical in terms of the related [Formula: see text]-radical.

scholarly journals Differential polynomial rings over rings satisfying a polynomial identity

2015 ◽  
Vol 423 ◽  
pp. 28-36 ◽  
Author(s):  
Jason P. Bell ◽  
Blake W. Madill ◽  
Forte Shinko
Keyword(s):  
Polynomial Identity ◽  
Differential Polynomial ◽  
Polynomial Rings
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