A concept unifying the Armendariz and NI conditions
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We study the structure of the set of nilpotent elements in various kinds of ring and introduce the concept of NR ring as a generalization of Armendariz rings and NI rings. We determine the precise relationships between NR rings and related ring-theoretic conditions. The [문자]othe's conjecture is true for the class of NR rings. We examined whether several kinds of extensions preserve the NR condition. The classical right quotient ring of an NR ring is also studied under some conditions on the subset of nilpotent elements.
Abstract
We study the structure of the set of nilpotent elements in various kinds of ring and introduce the concept of NR ring as a generalization of Armendariz rings and NI rings. We determine the precise relationships between NR rings and related ring-theoretic conditions. The [문자]othe's conjecture is true for the class of NR rings. We examined whether several kinds of extensions preserve the NR condition. The classical right quotient ring of an NR ring is also studied under some conditions on the subset of nilpotent elements.
참고문헌 (25)
- D. D. Anderson, "Armendariz rings and Gaussian rings", Comm. Algebra, 26(7), pp.2265~2272 (1998)
- R. Antoine, "Nilpotent elements and Armendariz rings", J. Algebra, 319(8), pp.3128~3140 (2008)
- E. P. Armendariz, "A note on extensions of Baer and P.P.-rings", J. Austral. Math. Soc, 18, pp.470~473 (1974)
- E. P. Armendariz, "Isomorphic Ore extensions", Comm. Algebra, 15(12), pp.2633~2652 (1987)
- G. F. Birkenmeier, "Completely prime ideals and asso- ciated radicals, (English summary) Ring theory (Granville, OH, 1992)", pp.102~129 (1993), World Sci. Publ
- G. F. Birkenmeier, "Regularity conditions and the simplicity of prime factor rings", J. Pure Appl. Algebra, 115(3), pp.213~230 (1997)
- V. Camillo, "McCoy rings and zero-divisors", J. Pure Appl. Algebra, 212(3), pp.599~615 (2008)
- Y. U. Cho, "Classical quotient rings and ordinary extensions of 2-primal rings", Algebra Colloq, 13(3), pp.513~523 (2006)
- K. R. Goodearl, "Von Neumann Regular Rings, Monographs and Studies in Mathematics", pp.4~ (1979), Pitman (Advanced Publishing Program)
- K. R. Goodearl, "An Introduction to Noncommutative Noetherian Rings", pp.16~ (1989), Cambridge University Press
- C. Y. Hong, "Ore extensions of Baer and p.p.-rings", J. Pure Appl. Algebra, 151(3), pp.215~226 (2000)
- C. Huh, "Armendariz rings and semicommutative rings", Comm. Algebra, 30(2), pp.751~761 (2002)
- S. U. Hwang, "Structure and topological conditions of NI rings", J. Algebra, 302(1), pp.186~199 (2006)
- Young Cheol Jeon, "On weak Armendariz rings", 대한수학회보, 46(1), pp.135~146 (2009), 대한수학회
- N. K. Kim, "Nilideals and nil-Armendariz rings"
- J. Krempa, "Some examples of reduced rings", Algebra Colloq, 3(4), pp.289~300 (1996)
- C. I. Lee, "Properties and related conditions of K-rings"
- T.-K. Lee, "On Armendariz rings", Houston J. Math, 29(3), pp.583~593 (2003)
- Y. Lee, "Questions on 2-primal rings", Comm. Algebra, 26(2), pp.595~600 (1998)
- G. Marks, "On 2-primal Ore extensions", Comm. Algebra, 29(5), pp.2113~2123 (2001)
- G. Marks, "A taxonomy of 2-primal rings", J. Algebra, 266(2), pp.494~520 (2003)
- M. Morse, "Symbolic dynamics", Amer. J. Math, 60, pp.815~866 (1936)
- M. B. Rege, "Armendariz rings", Proc. Japan Acad. Ser. A Math. Sci, 73(1), pp.14~17 (1997)
- L. H. Rowen, "Ring Theory" (1991), Academic Press, Inc
- A. Smoktunowicz, "Polynomial rings over nil rings need not be nil", J. Algebra, 233(2), pp.427~436 (2000)