RIGIDNESS AND EXTENDED ARMENDARIZ PROPERTY

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 48, Issue 1, 2011, pp.157-167
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2011.48.1.157

Title & Authors

RIGIDNESS AND EXTENDED ARMENDARIZ PROPERTY

Baser, Muhittin; Kaynarca, Fatma; Kwak, Tai-Keun;

Baser, Muhittin; Kaynarca, Fatma; Kwak, Tai-Keun;

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

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