Glasnik Matematicki, Vol. 49, No. 1 (2014), 47-51.


Malik Bataineh and D. D. Anderson

Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan

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.

2010 Mathematics Subject Classification.   13B25.

Key words and phrases.   Idealization, trivial extension, polynomial identity.

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DOI: 10.3336/gm.49.1.05


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