Original scientific paper

https://doi.org/10.3336/gm.49.1.05

Idealization and polynomial identities

Malik Bataineh orcid.org/0000-0002-6313-0203 ; Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan
D. D. Anderson ; Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA

Abstract

Let R be a commutative ring, let M be an R-module, let f(X1, …,Xn) be a polynomial (with coefficients from R or Z) and let k be a positive integer. We show that if R satisfies the polynomial identity
∏i=1kf(X1i, …,Xni)=0,
then the idealization R(+)M satisfies
∏i=1k+1f(X1i, …,Xni)=0.

Keywords

Idealization; trivial extension; polynomial identity

Hrčak ID:

122519

URI

https://hrcak.srce.hr/122519

Publication date:

8.6.2014.

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