On coefficients of nilpotent polynomials in skew polynomial rings
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We observe the basic structure of the products of coecients of nilpotent (left) polynomials in skew polynomial rings. This study consists of a process to extend a well-known result forsemi-Armendariz rings. We introduce the concept of α-skew n-semi-Armendariz ring, where α is a ring endomorphism. We prove thata ring R is α-rigid if and only if the n by n upper triangular matrixring over R is α-skew n-semi-Armendariz. This result are applicableto several known results.
Abstract
We observe the basic structure of the products of coecients of nilpotent (left) polynomials in skew polynomial rings. This study consists of a process to extend a well-known result forsemi-Armendariz rings. We introduce the concept of α-skew n-semi-Armendariz ring, where α is a ring endomorphism. We prove thata ring R is α-rigid if and only if the n by n upper triangular matrixring over R is α-skew n-semi-Armendariz. This result are applicableto several known results.
참고문헌 (13)
- D.D. Anderson, "Armendariz rings and Gaussian rings", Comm. Al- gebra, 26, pp.2265~2272 (1998)
- D.D. Anderson, "Semigroups and rings whose zero products commute", Comm. Algebra, 27, pp.2847~2852 (1999)
- E.P. Armendariz, "A note on extensions of Baer and P.P.-rings", J. Austral. Math. Soc, 18, pp.470~473 (1974)
- Y. Hirano, "On annihilator ideals of a polynomial ring over a noncommutative ring", J. Pure Appl. Algebra, 168, pp.45~52 (2002)
- C.Y. Hong, "On skew Armendariz rings", Comm. Algebra, 31, pp.103~122 (2003)
- C.Y. Hong, "Ore extensions of Baer and p.p.-rings", J. Pure and Appl. Algebra, 151, pp.215~226 (2000)
- C. Huh, "A. Smoktunowicz, Armendariz rings and semicommutative rings", Comm. Algebra, 30, pp.751~761 (2002)
- 전영철, "A STRUCTURE ON COEFFICIENTS OF NILPOTENT POLYNOMIALS", 대한수학회지, 47(4), pp.719~733 (2010), 대한수학회
- N.K. Kim, "Armendariz rings and reduced rings", J. Algebra, 223, pp.477~488 (2000)
- J. Krempa, "Some examples of reduced rings", Algebra Colloq, 3, pp.289~300 (1996)
- J. Lambek, "On the representation of modules by sheaves of factor modules", Canad. Math. Bull, 14, pp.359~368 (1971)
- T.-K. Lee, "On Armendariz rings", Houston J. Math, 2, pp.583~593 (2003)
- M.B. Rege, "Armendariz rings", Proc. Japan Acad. Ser. A Math. Sci, 73, pp.14~17 (1997)