On weak Armendariz ideals
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We introduce weak Armendariz ideals which are a generalization of ideals have the weakly insertion of factors property (or simply weakly IFP) and investigate their properties. Moreover, we prove that, if I is a weak Armendariz ideal of R, then I[x] is a weak Armendariz ideal of R[x]. As a consequence, we show that, R is weak Armendariz if and only if R[x] is a weak Armendariz ring. Also we obtain a generalization of [8] and [9].
Abstract
We introduce weak Armendariz ideals which are a generalization of ideals have the weakly insertion of factors property (or simply weakly IFP) and investigate their properties. Moreover, we prove that, if I is a weak Armendariz ideal of R, then I[x] is a weak Armendariz ideal of R[x]. As a consequence, we show that, R is weak Armendariz if and only if R[x] is a weak Armendariz ring. Also we obtain a generalization of [8] and [9].
참고문헌 (11)
- D. D. Anderson, "Armendariz rings and Gaussian rings", Comm. Algebra, 26(7), pp.2265~2272 (1998)
- E. P. Armendariz, "A note on extensions of Baer and P.P.-rings", J. Austral. Math. Soc, 18, pp.470~473 (1974)
- C. Y. Hong, "On skew Armendariz rings", Comm. Algebra, 31(1), pp.103~122 (2003)
- C. Huh, "P.P.-rings and generalized P.P.-rings", J. Pure Appl. Algebra, 167(1), pp.37~52 (2002)
- C. Huh, "Armendariz rings and semicommutative rings", Comm. Algebra, 30(2), pp.751~761 (2002)
- N. K. Kim, "Armendariz rings and reduced rings", J. Algebra, 223(2), pp.477~488 (2000)
- T. K. Lee, "On Armendariz rings", Houston J. Math, 29(3), pp.583~593 (2003)
- L. Liang, "On a generalization of semicommutative rings", Taiwanese J. Math, 11(5), pp.1359~1368 (2007)
- Z. Liu, "On weak Armendariz rings", Comm. Algebra, 34(7), pp.2607~2616 (2006)
- G. Mason, "Reflexive ideals", Comm. Algebra, 9(17), pp.1709~1724 (1981)
- M. B. Rege, "Armendariz rings", Proc. Japan Acad. Ser. A Math. Sci, 73(1), pp.14~17 (1997)