Reversibility over prime radicals
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The studies of reversible and 2-primal rings have done important roles in noncommutative ring theory. We in this note introduce the concept of it quasi-reversible-over-prime-radical (simply, it QRPR) as a generalization of the 2-primal ring property. A ring is called it QRPR if ab=0 for a, bin R implies that ab is contained in the prime radical. In this note we study the structure of QRPR rings and examine the QRPR property of several kinds of ring extensions which have roles in noncommutative ring theory.
Abstract
The studies of reversible and 2-primal rings have done important roles in noncommutative ring theory. We in this note introduce the concept of it quasi-reversible-over-prime-radical (simply, it QRPR) as a generalization of the 2-primal ring property. A ring is called it QRPR if ab=0 for a, bin R implies that ab is contained in the prime radical. In this note we study the structure of QRPR rings and examine the QRPR property of several kinds of ring extensions which have roles in noncommutative ring theory.
참고문헌 (21)
- D.D. Anderson, "Semigroups and rings whose zero products commute", Comm. Algebra, 27, pp.2847~2852 (1999)
- D.D. Anderson, "Armendariz rings and gaussian rings", Comm. Algebra, 26, pp.2265~2272 (1998)
- R. Antoine, "Nilpotent elements and Armendariz rings", J. Algebra, pp.3128~3140 (2008)
- 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. Austral. Math. Soc, 2, pp.363~368 (1970)
- G.F. Birkenmeier, "Completely prime ideals and associated radicals", Proc. Biennial Ohio State-Denison Conference 1992, pp.102~129 (1992), World Scientific
- W. Chen, "On nil-semicommutative rings", Thai J. M, 9, pp.39~47 (2011)
- P.M. Cohn, "Reversible rings", Bull. London Math. Soc, 31, pp.641~648 (1999)
- N.J. Divinsky, "Rings and Radicals" (1965), University of Toronto Press
- Y. Hirano, "On rings whose prime radical contains all nilpotent elements of index two", Arch. Math, 66, pp.360~365 (1996)
- C. Huh, "P. P.-rings and generalized P. P.-rings", J. Pure Appl. Algebra, 167, pp.37~52 (2002)
- S.U. Hwang, "Structure and topological conditions of NI rings", J. Algebra, 302, pp.186~199 (2006)
- N.K. Kim, "Armendariz rings and reduced rings", J. Algebra, 223, pp.477~488 (2000)
- T.Y. Lam, "A First Course in Noncommutative Rings" (1991), Springer-Verlag
- J. Lambek, "On the representation of modules by sheaves of factor modules", Canad. Math. Bull, 14, pp.359~368 (1971)
- L.Liang, "On a generalization of semicommutative rings", Taiwanese J, Math, 11, pp.1359~1368 (2007)
- G. Marks, "On 2-primal Ore extensions", Comm. Algebra, 29, pp.2113~2123 (2001)
- L. Motais de Narbonne, "Anneaux semi-commutatifs et unis riels anneaux dont les id aux principaux sont idempotents", Proceedings of the 106th National Congress of Learned Societies, pp.71~73 (1982)
- M.B. Rege, "Armendariz rings", Proc. Japan Acad. Ser. A Math. Sci, 73, pp.14~17 (1997)
- L.H. Rowen, "Ring Theory" (1991), Academic Press, Inc.
- G. Shin, "Prime ideals and sheaf representation of a pseudo symmetric ring", Trans. Amer. Math. Soc, 184, pp.43~60 (1973)