Rocky Mountain Journal of Mathematics

Amitsur's property for skew polynomials of derivation type

Chan Yong Hong, Nam Kyun Kim, Yang Lee, and Pace P. Nielsen

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Abstract

We investigate when radicals $\mathfrak {F}$ satisfy Amit\-sur's property on skew polynomials of derivation type, namely, $\mathfrak {F}(R[x;\delta ])=(\mathfrak {F}(R[x;\delta ])\cap R)[x;\delta ].$ In particular, we give a new argument that the Brown-McCoy radical has this property. We also give a new characterization of the prime radical of $R[x;\delta ]$.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 7 (2017), 2197-2218.

Dates
First available in Project Euclid: 24 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1514084425

Digital Object Identifier
doi:10.1216/RMJ-2017-47-7-2197

Mathematical Reviews number (MathSciNet)
MR3748228

Zentralblatt MATH identifier
1383.16028

Subjects
Primary: 16S36: Ordinary and skew polynomial rings and semigroup rings [See also 20M25]
Secondary: 16N60: Prime and semiprime rings [See also 16D60, 16U10] 16N80: General radicals and rings {For radicals in module categories, see 16S90} 16S20: Centralizing and normalizing extensions

Keywords
Amitsur's property Brown-McCoy radical derivation prime radical skew polynomial

Citation

Hong, Chan Yong; Kim, Nam Kyun; Lee, Yang; Nielsen, Pace P. Amitsur's property for skew polynomials of derivation type. Rocky Mountain J. Math. 47 (2017), no. 7, 2197--2218. doi:10.1216/RMJ-2017-47-7-2197. https://projecteuclid.org/euclid.rmjm/1514084425


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