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

Juncheol Han, Yui-yun Jung, Yang Lee, hyo jin Sung

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.

Keywords


INFP ring, nilpotent, idempotent, IFP ring, Abelian ring

Subject classification

16N40, 16U80

Sponsor(s)

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

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References


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

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

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

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

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

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

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)

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

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)

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)

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

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

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

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)

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

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


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