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RIGIDNESS AND EXTENDED ARMENDARIZ PROPERTY
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 Title & Authors
RIGIDNESS AND EXTENDED ARMENDARIZ PROPERTY
Baser, Muhittin; Kaynarca, Fatma; Kwak, Tai-Keun;
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 Abstract
For a ring endomorphism of a ring R, Krempa called rigid endomorphism if = 0 implies a = 0 for a R, and Hong et al. called R an -rigid ring if there exists a rigid endomorphism . Due to Rege and Chhawchharia, a ring R is called Armendariz if whenever the product of any two polynomials in R[x] over R is zero, then so is the product of any pair of coefficients from the two polynomials. The Armendariz property of polynomials was extended to one of skew polynomials (i.e., -Armendariz rings and -skew Armendariz rings) by Hong et al. In this paper, we study the relationship between -rigid rings and extended Armendariz rings, and so we get various conditions on the rings which are equivalent to the condition of being an -rigid ring. Several known results relating to extended Armendariz rings can be obtained as corollaries of our results.
 Keywords
reduced rings;skew polynomial rings;rigid rings;(extended) Armendariz rings;trivial extension;semiprime rings;semicommutative rings;
 Language
English
 Cited by
1.
On α-nilpotent elements and α-Armendariz rings, Journal of Algebra and Its Applications, 2015, 14, 05, 1550064  crossref(new windwow)
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