Korean J. Math. Vol. 22 No. 4 (2014) pp.611-619
DOI: https://doi.org/10.11568/kjm.2014.22.4.611

Insertion-of-Factors-Property with factors nilpotents

Article Sidebar

PDF
Published: Dec 26, 2014
Keywords:
INFP ring, nilpotent, idempotent, IFP ring, Abelian ring
Mathematics Subject Classification:
16N40, 16U80

Main Article Content

Juncheol Han
Pusan National University
Yui-yun Jung
Pusan National University
Yang Lee
Pusan National University
hyo jin Sung
Pusan National University

Abstract

We in this note study a ring theoretic property which unies Armendariz and IFP. We call this new concept INFP. We rst show that idempotents and nilpotents are connected by the Abelian ring property. Next the structure of INFP rings is studied in relation to several sorts of algebraic systems.


Article Details

Supporting Agencies

This work was supported by a 2-Year Research Grant of Pusan National Univer- sity.

References

[1] R. Antoine, Nilpotent elements and Armendariz rings, J. Algebra 319 (2008), 3128–3140. Google Scholar

[2] E.P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Austral. Math. Soc. 18 (1974), 470–473. Google Scholar

[3] H.E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2 (1970), 363–368. Google Scholar

[4] G.M. Bergman, Coproducts and some universal ring constructions, Tran. Amer. Math. Soc. 200 (1974), 33–88. Google Scholar

[5] G.M. Bergman, Modules over coproducts of rings, Trans. Amer. Math. Soc. 200 (1974), 1–32. Google Scholar

[6] K.R. Goodearl, Von Neumann Regular Rings, Pitman, London (1979). Google Scholar

[7] C. Huh, H.K. Kim, Y. Lee, p.p. rings and generalized p.p. rings, J. Pure Appl. Algebra 167 (2002), 37–52. Google Scholar

[8] C. Huh, Y. Lee, A. Smoktunowicz, Armendariz rings and semicommutative ring, Comm. Algebra 30 (2002), 751-761. Google Scholar

[9] Y.C. Jeon, H.K. Kim, Y. Lee, J.S. Yoon, On weak Armendariz rings, Bull. Korean Math. Soc. 46 (2009), 135–146. Google Scholar

[10] D.W. Jung, N.K. Kim, Y. Lee, S.P. Yang, Nil-Armendariz rings and upper nil-radicals, Internat. J. Math. Comput. 22 (2012), 1250059 (1–13). Google Scholar

[11] N.K. Kim, Y. Lee, Armendariz rings and reduced rings, J. Algebra 223 (2000), 477–488. Google Scholar

[12] N.K. Kim, Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra 185 (2003), 207–223. Google Scholar

[13] G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), 2113–2123. Google Scholar

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

[15] M.B. Rege, S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), 14–17. Google Scholar

[16] G. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973), 43–60. Google Scholar