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A STRUCTURE ON COEFFICIENTS OF NILPOTENT POLYNOMIALS
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 Title & Authors
A STRUCTURE ON COEFFICIENTS OF NILPOTENT POLYNOMIALS
Jeon, Young-Cheol; Lee, Yang; Ryu, Sung-Ju;
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 Abstract
We observe a structure on the products of coefficients of nilpotent polynomials, introducing the concept of n-semi-Armendariz that is a generalization of Armendariz rings. We first obtain a classification of reduced rings, proving that a ring R is reduced if and only if the n by n upper triangular matrix ring over R is n-semi-Armendariz. It is shown that n-semi-Armendariz rings need not be (n+1)-semi-Armendariz and vice versa. We prove that a ring R is n-semi-Armendariz if and only if so is the polynomial ring over R. We next study interesting properties and useful examples of n-semi-Armendariz rings, constructing various kinds of counterexamples in the process.
 Keywords
n-semi-Armendariz ring;polynomial ring;reduced ring;Armendariz ring;triangular matrix ring;
 Language
English
 Cited by
1.
ON COEFFICIENTS OF NILPOTENT POLYNOMIALS IN SKEW POLYNOMIAL RINGS,;;;

Korean Journal of Mathematics, 2013. vol.21. 4, pp.421-428 crossref(new window)
2.
ON SEMI-ARMENDARIZ MATRIX RINGS,;;

대한수학회지, 2015. vol.52. 4, pp.781-795 crossref(new window)
1.
On a ring structure related to annihilators, Journal of Algebra and Its Applications, 2016, 1750156  crossref(new windwow)
2.
ON SEMI-ARMENDARIZ MATRIX RINGS, Journal of the Korean Mathematical Society, 2015, 52, 4, 781  crossref(new windwow)
3.
ON COEFFICIENTS OF NILPOTENT POLYNOMIALS IN SKEW POLYNOMIAL RINGS, Korean Journal of Mathematics, 2013, 21, 4, 421  crossref(new windwow)
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