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IFP RINGS AND NEAR-IFP RINGS
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 Title & Authors
IFP RINGS AND NEAR-IFP RINGS
Ham, Kyung-Yuen; Jeon, Young-Cheol; Kang, Jin-Woo; Kim, Nam-Kyun; Lee, Won-Jae; Lee, Yang; Ryu, Sung-Ju; Yang, Hae-Hun;
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 Abstract
A ring R is called IFP, due to Bell, if ab=0 implies aRb=0 for . Huh et al. showed that the IFP condition need not be preserved by polynomial ring extensions. But it is shown that is a nonzero nilpotent ideal of E whenever R is an IFP ring and is nilpotent, where E is a polynomial ring over R, F is a polynomial ring over E, and are the coefficients of f. we shall use the term near IFP to denote such a ring as having place near at the IFPness. In the present note the structures of IFP rings and near-IFP rings are observed, extending the classes of them. IFP rings are NI (i.e., nilpotent elements form an ideal). It is shown that the near-IFPness and the NIness are distinct each other, and the relations among them and related conditions are examined.
 Keywords
IFP ring;near-IFP ring;reduced ring;NI ring;polynomial ring;matrix ring;nilpotent ideal;
 Language
English
 Cited by
1.
ON CONDITIONS PROVIDED BY NILRADICALS,;;;;;;

대한수학회지, 2009. vol.46. 5, pp.1027-1040 crossref(new window)
1.
On Commutativity of Semiprime Right Goldie C<i><sub>k</sub></i>-Rings, Advances in Pure Mathematics, 2012, 02, 04, 217  crossref(new windwow)
2.
ON CONDITIONS PROVIDED BY NILRADICALS, Journal of the Korean Mathematical Society, 2009, 46, 5, 1027  crossref(new windwow)
3.
ON SEMI-IFP RINGS, Korean Journal of Mathematics, 2015, 23, 1, 37  crossref(new windwow)
 References
1.
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)

2.
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

3.
D. B. Erickson, Orders for finite noncommutative rings, Amer. Math. Monthly 73 (1966), 376-377 crossref(new window)

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

5.
K. Y. Ham, C. Huh, Y. C. Hwang, Y. C. Jeon, H. K. Kim, S. M. Lee, Y. Lee, S. R. O, and J. S. Yoon, On weak Armendariz rings, submitted

6.
I. N. Herstein, Topics in Ring Theory, The University of Chicago Press, Chicago-London 1965

7.
C. Y. Hong, H. K. Kim, N. K. Kim, T. K. Kwak, Y. Lee, and K. S. Park, Rings whose nilpotent elements form a Levitzki radical ring, Comm. Algebra 35 (2007), no. 4, 1379-1390 crossref(new window)

8.
C. Y. Hong and T. K. Kwak, On minimal strongly prime ideals, Comm. Algebra 28 (2000), no. 10, 4867-4878 crossref(new window)

9.
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)

10.
C. Huh, H. K. Kim, D. S. Lee, and Y. Lee, Prime radicals of formal power series rings, Bull. Korean Math. Soc. 38 (2001), no. 4, 623-633

11.
C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761 crossref(new window)

12.
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)

13.
N. K. Kim and Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra 185 (2003), no. 1-3, 207-223 crossref(new window)

14.
A. A. Klein, Rings of bounded index, Comm. Algebra 12 (1984), no. 1-2, 9-21. crossref(new window)

15.
G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), no. 5, 2113-2123 crossref(new window)

16.
L. Motais de Narbonne, Anneaux semi-commutatifs et uniseriels; anneaux dont les ideaux principaux sont idempotents, Proceedings of the 106th National Congress of Learned Societies (Perpignan, 1981), 71-73, Bib. Nat., Paris, 1982

17.
G. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973), 43-60 crossref(new window)