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For a ring endomorphism α of a ring R, Krempa called α a rigid endomorphism if aα(a)=0 implies a=0 for a∈ R, and Hong et al. called R an α- rigid ring if there exists a rigid endomorphism α. 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.,α-Armendariz rings and α-skew Armendariz rings) by Hong et al. In this paper, we study the relationship between α-rigid rings and extended Armendariz rings, and so we get various conditions on the rings which are equivalent to the condition of being an α-rigid ring. Several known results relating to extended Armendariz rings can be obtained as corollaries of our results.
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참고문헌 (12)
참고문헌 신청
A. A. M. Kamal / 1994 / Some remarks on Ore extension rings / Comm. Algebra 22 (10) : 3637 ~ 3667
C. Y. Hong / 2000 / Ore extensions of Baer and p.p.-rings / J. Pure Appl. Algebra 151 (3) : 215 ~ 226
C. Y. Hong / 2003 / On skew Armendariz rings / Comm. Algebra 31 (1) : 103 ~ 122
E. P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Austral. Math. Soc 18 : 470 ~ 473
J. Krempa / 1996 / Some examples of reduced rings / Algebra Colloq 3 (4) : 289 ~ 300
C. Y. Hong / 2000 / Ore extensions of Baer and p.p.-rings / J. Pure Appl. Algebra 151 (3) : 215 ~ 226
C. Y. Hong / 2003 / On skew Armendariz rings / Comm. Algebra 31 (1) : 103 ~ 122
E. P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Austral. Math. Soc 18 : 470 ~ 473
J. Krempa / 1996 / Some examples of reduced rings / Algebra Colloq 3 (4) : 289 ~ 300
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