A remark on IFP rings
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We continue the study of power-Armendariz rings over IFP rings, introducing k-power Armendariz rings as a generalization of power-Armendariz rings. Han et al. showed that IFP rings are 1-power Armendariz. We prove that IFP rings are 2-power Armendariz. We moreover study a relationship between IFP rings and k-power Armendariz rings under a condition related to nilpotency of coefficients.
Abstract
We continue the study of power-Armendariz rings over IFP rings, introducing k-power Armendariz rings as a generalization of power-Armendariz rings. Han et al. showed that IFP rings are 1-power Armendariz. We prove that IFP rings are 2-power Armendariz. We moreover study a relationship between IFP rings and k-power Armendariz rings under a condition related to nilpotency of coefficients.
참고문헌 (9)
- D.D. Anderson, "Armendariz rings and Gaussian rings", Comm. Al- gebra, 26, pp.2265~2272 (1998)
- E.P. Armendariz, "A note on extensions of Baer and P.P.-rings", J. Aust. Math. Soc, 18, pp.470~473 (1974)
- H.E. Bell, "Near-rings in which each element is a power of itself", Bull. Aust. Math. Soc, 2, pp.363~368 (1970)
- J. Han, "On powers of coefficients of zero-dividing polynomials, (submitted)", ~
- C. Huh, "A. Smoktunowicz, Armendariz rings and semicommutative ring", Comm. Algebra, 30, pp.751~761 (2002)
- Young Cheol Jeon, "On weak Armendariz rings", 대한수학회보, 46(1), pp.135~146 (2009), 대한수학회
- N.K. Kim, "Armendariz rings and reduced rings", J. Algebra, 223, pp.477~488 (2000)
- T.K. Lee, "Armendariz and reduced rings", Comm. Algebra, 32, pp.2287~2299 (2004)
- M.B. Rege, "Armendariz rings", Proc. Japan Acad. Ser. A Math. Sci, 73, pp.14~17 (1997)