JOURNAL BROWSE
Search
Advanced SearchSearch Tips
MCCOY CONDITION ON IDEALS OF COEFFICIENTS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
MCCOY CONDITION ON IDEALS OF COEFFICIENTS
Cheon, Jeoung Soo; Huh, Chan; Kwak, Tai Keun; Lee, Yang;
  PDF(new window)
 Abstract
We continue the study of McCoy condition to analyze zero-dividing polynomials for the constant annihilators in the ideals generated by the coefficients. In the process we introduce the concept of ideal--McCoy rings, extending known results related to McCoy condition. It is shown that the class of ideal--McCoy rings contains both strongly McCoy rings whose non-regular polynomials are nilpotent and 2-primal rings. We also investigate relations between the ideal--McCoy property and other standard ring theoretic properties. Moreover we extend the class of ideal--McCoy rings by examining various sorts of ordinary ring extensions.
 Keywords
ideal--McCoy ring;strongly McCoy ring;-McCoy ring;poly-nomial ring;matrix ring;the classical right quotient ring;
 Language
English
 Cited by
 References
1.
D. D. Anderson and V. Camillo, Armendariz rings and gaussian rings, Comm. Algebra 26 (1998), no. 7, 2265-2272. crossref(new window)

2.
D. D. Anderson and V. Camillo, Semigroups and rings whose zero products commute, Comm. Algebra 27 (1999), no. 6, 2847-2852. 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.
H. E. Bell, Near-rings in which each element is a power of itself, Bull. Aust. Math. Soc. 2 (1970), 363-368. crossref(new window)

6.
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.

7.
V. Camillo and P. P. Nielsen, McCoy rings and zero-divisors, J. Pure Appl. Algebra 212 (2008), no. 3, 599-615. crossref(new window)

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 73 (1968), 512-514.

10.
K. R. Goodearl, Von Neumann Regular Rings, Pitman, London-San Francisco-Mel-bourne, 1979.

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

12.
C. Y. Hong, Y. C. Jeon, N. K. Kim, and Y. Lee, The McCoy condition on noncommutative rings, Comm. Algebra 39 (2011), no. 5, 1809-1825. crossref(new window)

13.
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)

14.
Y. C. Jeon, H. K. Kim, Y. Lee, and J. S. Yoon, On weak Armendariz rings, Bull. Korean Math. Soc. 46 (2009), no. 1, 135-146. crossref(new window)

15.
Y. C. Jeon, H. K. Kim, N. K. Kim, T. K. Kwak, Y. Lee, and D. E. Yeo, On a generalization of the McCoy condition, J. Korean Math. Soc. 47 (2010), no. 6, 1269-1282. crossref(new window)

16.
N. K. Kim and Y. Lee, On a ring property unifying reversible and right duo rings, J. Korean Math. Soc. (to appear). crossref(new window)

17.
N. K. Kim and Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra 185 (2003), no. 1-3, 207-223. crossref(new window)

18.
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)

19.
Z. Lei, J. Chen, and Z. Ying, A question on McCoy rings, Bull. Aust. Math. Soc. 76 (2007), no. 1, 137-141. crossref(new window)

20.
J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, John Wiley & Sons Ltd., 1987.

21.
N. H. McCoy, Remarks on divisors of zero, Amer. Math. Monthly 49 (1942), 286-295. crossref(new window)

22.
P. P. Nielsen, Semi-commutativity and the McCoy condition, J. Algebra 298 (2006), no. 1, 134-141. crossref(new window)

23.
M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 1, 14-17. crossref(new window)

24.
G. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973), 43-60. crossref(new window)