JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON A GENERALIZATION OF MCCOY RINGS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON A GENERALIZATION OF MCCOY RINGS
Camillo, Victor; Kwak, Tai Keun; Lee, Yang;
  PDF(new window)
 Abstract
Rege-Chhawchharia, and Nielsen introduced the concept of right McCoy ring, based on the McCoy's theorem in 1942 for the annihilators in polynomial rings over commutative rings. In the present note we concentrate on a natural generalization of a right McCoy ring that is called a right nilpotent coefficient McCoy ring (simply, a right NC-McCoy ring). The structure and several kinds of extensions of right NC-McCoy rings are investigated, and the structure of minimal right NC-McCoy rings is also examined.
 Keywords
right (NC-)McCoy ring;polynomial ring;NI ring;minimal right NC-McCoy ring;
 Language
English
 Cited by
 References
1.
S. A. Amitsur, Radicals of polynomials rings, Canad. J. Math. 8 (1956), 355-361. crossref(new window)

2.
D. D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), no. 7, 2265-2272. crossref(new window)

3.
R. Antoine, Nilpotent elements and Armendariz rings, J. Algebra 319 (2008), no. 8, 3128-3140. crossref(new window)

4.
E. P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Aust. Math. Soc. 18 (1974), 470-473. crossref(new window)

5.
G. F. Birkenmeier, H. E. Heatherly, and E. K. Lee, Completely prime ideals and associated radicals, Ring theory (Granville, OH, 1992), 102-129, World Sci. Publ., River Edge, NJ, 1993.

6.
V. Camillo and P. P. Nielsen, McCoy rings and zero-divisors, J. Pure Appl. Algebra 212 (2008), no. 3, 599-615. crossref(new window)

7.
A. W. Chatters and C. R. Hajarnavis, Rings with Chain Conditions, Pitman Advanced Publishing Program, 1980.

8.
P. M. Cohn, Reversible rings, Bull. London Math. Soc. 31 (1999), no. 6, 641-648. crossref(new window)

9.
K. E. Eldridge, Orders for finite noncommutative rings with unity, Amer. Math. Monthly 75 (1968), 512-514. crossref(new window)

10.
S. Ghalandarzadeh and M. Khoramdel, On weak McCoy rings, Thai J. Math. 6 (2008), no. 2, 337-342.

11.
K. R. Goodearl and R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, 1989.

12.
R. Gordon and J. C. Robson, Krull dimension, Memoirs of the American Mathematical Society, No. 133. American Mathematical Society, Providence, R.I., 1973.

13.
C. Y. Hong and T. K. Kwak, On minimal strongly prime ideals, Comm. Algebra 28 (2000), no. 10, 4867-4878. crossref(new window)

14.
C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761. crossref(new window)

15.
S. U. Hwang, Y. C. Jeon, and Y. Lee, Structure and topological conditions of NI rings, J. Algebra 302 (2006), no. 1, 186-199. crossref(new window)

16.
L. G. Jones and L. Weiner, Advanced Problems and Solutions: Solutions: 4419 , Amer. Math. Monthly 59 (1952), no. 5, 336-337. crossref(new window)

17.
D. W. Jung, N. K. Kim, and Y. Lee, Nil-Armendariz rings and upper nilradicals, Internat. J. Algebra Comput. 22 (2012), no. 6, 1250059, 13 pp. crossref(new window)

18.
A. A. Klein, Rings of bounded index, Comm. Algebra 12 (1984), no. 1-2, 9-21. crossref(new window)

19.
J. Krempa, Radicals of semi-group rings, Fund. Math. 85 (1974), no. 1, 57-71.

20.
R. L. Kruse and D. T. Price, Nilpotent Rings, Gordon and Breach, New York, London, Paris, 1969.

21.
T. K. Kwak and Y. Lee, Rings over which coefficients of nilpotent polynomials are nilpotent, Internat. J. Algebra Comput. 21 (2011), no. 5, 745-762. crossref(new window)

22.
J. Lambek, Lectures on Rings and Modules, Blaisdell Publishing Company, Waltham, 1966.

23.
C. Lanski, Nil subrings of Goldie rings are nilpotent, Canad. J. Math. 21 (1969), 904- 907. crossref(new window)

24.
T. H. Lenagan, Nil ideals in rings with finite Krull dimensions, J. Algebra 29 (1974), 77-87. crossref(new window)

25.
Z. Liu and R. Zhao, On Weak Armendariz Rings, Comm. Algebra 34 (2006), no. 7, 2607-2616. crossref(new window)

26.
G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), no. 5, 2113-2123. crossref(new window)

27.
N. H. McCoy, Remarks on divisors of zero, Amer. Math. Monthly 49 (1942), 286-295. crossref(new window)

28.
L. Motais de Narbonne, Anneaux semi-commutatifs et unis riels anneaux dont les id aux principaux sont idempotents, In: Proceedings of the 106th National Congress of Learned Societies (Perpignan, 1981), Bib. Nat., Paris (1982), 71-73.

29.
P. P. Nielsen, Semi-commutativity and the McCoy condition, J. Algebra 298 (2006), no. 1, 134-141. crossref(new window)

30.
M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 1, 14-17. crossref(new window)

31.
A. Smoktunowicz, Polynomial rings over nil rings need not be nil, J. Algebra 233 (2000), no. 2, 427-436. crossref(new window)