JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON CONDITIONS PROVIDED BY NILRADICALS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON CONDITIONS PROVIDED BY NILRADICALS
Kim, Hong-Kee; Kim, Nam-Kyun; Jeong, Mun-Seob; Lee, Yang; Ryu, Sung-Ju; Yeo, Dong-Eun;
  PDF(new window)
 Abstract
A ring R is called IFP, due to Bell, if ab = 0 implies aRb = 0 for a, b R. Huh et al. showed that the IFP condition is not preserved by polynomial ring extensions. In this note we concentrate on a generalized condition of the IFPness that can be lifted up to polynomial rings, introducing the concept of quasi-IFP rings. The structure of quasi-IFP rings will be studied, characterizing quasi-IFP rings via minimal strongly prime ideals. The connections between quasi-IFP rings and related concepts are also observed in various situations, constructing necessary examples in the process. The structure of minimal noncommutative (quasi-)IFP rings is also observed.
 Keywords
IFP ring;quasi-IFP ring;Wedderburn radical;nilradical;polynomial ring;
 Language
English
 Cited by
1.
ON WEAK ZIP SKEW POLYNOMIAL RINGS, Asian-European Journal of Mathematics, 2012, 05, 03, 1250039  crossref(new windwow)
2.
On Commutativity of Semiprime Right Goldie C<i><sub>k</sub></i>-Rings, Advances in Pure Mathematics, 2012, 02, 04, 217  crossref(new windwow)
 References
1.
A. Badawi, On abelian $\pi$-regular rings, Comm. Algebra 25 (1997), no. 4, 1009.1021 crossref(new window)

2.
H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2 (1970), 363.368 crossref(new window)

3.
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

4.
A. W. Chatters and C. R. Hajarnavis, Rings with Chain Conditions, Research Notes in Mathematics, 44. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1980

5.
N. J. Divinsky, Rings and Radicals, Mathematical Expositions No. 14 University of Toronto Press, Toronto, Ont. 1965

6.
D. B. Erickson, Orders for finite noncommutative rings, Amer. Math. Monthly 73 (1966), 376.377 crossref(new window)

7.
K. R. Goodearl, von Neumann Regular Rings, Monographs and Studies in Mathematics, 4. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979

8.
K.-Y. Ham, Y. C. Jeon, J. Kang, N. K. Kim, W. Lee, Y. Lee, S. J. Ryu, and H.-H. Yang, IFP Rings and Near-IFP Rings, J. Korean Math. Soc. 45 (2008), no. 3, 727.740 crossref(new window)

9.
C. Y. Hong and T. K. Kwak, On minimal strongly prime ideals, Comm. Algebra 28 (2000), no. 10, 4867.4878 crossref(new window)

10.
C. Huh, H. K. Kim, and Y. Lee, p.p. rings and generalized p.p. rings, J. Pure Appl. Algebra 167 (2002), no. 1, 37.52 crossref(new window)

11.
C. Huh, N. K. Kim, and Y. Lee, Examples of strongly $\pi$-regular rings, J. Pure Appl. Algebra 189 (2004), no. 1-3, 195.210 crossref(new window)

12.
C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751.761 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.
S. U. Hwang, N. K. Kim, and Y. Lee, On rings whose right annihilators are bounded, Glasgow Math. J., To appear crossref(new window)

15.
Y. C. Jeon, H. K. Kim, and J. S. Yoon, On weak Armendariz rings, Bull. Korean Math. Soc. 46 (2009), no. 1, 135.146 crossref(new window)

16.
N. K. Kim and Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra 185 (2003), no. 1-3, 207.223 crossref(new window)

17.
N. K. Kim, Y. Lee, and S. J. Ryu, An ascending chain condition on Wedderburn radicals, Comm. Algebra 34 (2006), no. 1, 37.50 crossref(new window)

18.
J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull. 14 (1971), 359.368 crossref(new window)

19.
C. Lanski, Nil subrings of Goldie rings are nilpotent, Canad. J. Math. 21 (1969), 904. 907 crossref(new window)

20.
G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), no. 5, 2113.2123 crossref(new window)

21.
L. Motais de Narbonne, Anneaux semi-commutatifs et $unis{\acute{e}}riels$; anneaux dont les $id{\acute{e}}aux$ principaux sont idempotents, Proceedings of the 106th National Congress of Learned Societies (Perpignan, 1981), 71.73, Bib. Nat., Paris, 1982

22.
L. H. Rowen, Ring Theory, Academic Press, Inc., Boston, MA, 1991

23.
G. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973), 43.60 crossref(new window)

24.
W. Xue, On strongly right bounded finite rings, Bull. Austral. Math. Soc. 44 (1991), no. 3, 353.355 crossref(new window)

25.
W. Xue, Structure of minimal noncommutative duo rings and minimal strongly bounded nonduo rings, Comm. Algebra 20 (1992), no. 9, 2777.2788 crossref(new window)