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

IDEALIZATION AND POLYNOMIAL IDENTITIES

Malik Bataineh and D. D. Anderson

Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan
e-mail: msbataineh@just.edu.jo

Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA
e-mail: dan-anderson@uiowa.edu

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.

Full text (PDF) (free access)

DOI: 10.3336/gm.49.1.05

References:

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    MathSciNet     CrossRef

  3. A. L. Foster, The idempotent elements of a commutative ring form a Boolean algebra; ring duality and transformation theory, Duke Math. J. 12 (1945), 143-152.
    MathSciNet     CrossRef

  4. A. L. Foster, The theory of Boolean-like rings, Trans. Amer. Math. Soc. 59 (1946), 166-187.
    MathSciNet     CrossRef

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