Rigidness and extended Armendariz property
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
Abstract
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.
참고문헌 (12)
- E. P. Armendariz, "A note on extensions of Baer and P.P.-rings", J. Austral. Math. Soc, 18, pp.470~473 (1974)
- W. Chen, "A note on skew Armendariz rings", Comm. Algebra, 33(4), pp.1137~1140 (2005)
- W. Chen, "On skew Armendariz rings and rigid rings", Houston J. Math, 33(2), pp.341~353 (2007)
- C. Y. Hong, "Ore extensions of Baer and p.p.-rings", J. Pure Appl. Algebra, 151(3), pp.215~226 (2000)
- C. Y. Hong, "On skew Armendariz rings", Comm. Algebra, 31(1), pp.103~122 (2003)
- 곽태근, "Extensions of generalized Armendariz rings", ALGEBRA COLLOQUIUM, 13(2), pp.253~266
- A. A. M. Kamal, "Some remarks on Ore extension rings", Comm. Algebra, 22(10), pp.3637~3667 (1994)
- N. K. Kim, "Armendariz rings and reduced rings", J. Algebra, (2), pp.477~488 (2000)
- J. Krempa, "Some examples of reduced rings", Algebra Colloq, 3(4), pp.289~300 (1996)
- T. K. Lee, "On Armendariz rings", Houston J. Math, 29(3), pp.583~593 (2003)
- T. K. Lee, "Armendariz and reduced rings", Comm. Algebra, 32(6), pp.2287~2299 (2004)
- M. B. Rege, "Armendariz rings", Proc. Japan Acad. Ser. A Math. Sci, 73(1), pp.14~17 (1997)