Korean J. Math. Vol. 24 No. 4 (2016) pp.737-750
DOI: https://doi.org/10.11568/kjm.2016.24.4.737

Abelian property concerning factorization modulo radicals

Main Article Content

Dong Hyeon Chae
Jeong Min Choi
Dong Hyun Kim
Jae Eui Kim
Jae Min Kim
Tae Hyeong Kim
Ji Young Lee
Yang Lee
You Sun Lee
Jin Hwan Noh
Sung Ju Ryu

Abstract

In this note we describe some classes of rings in relation to Abelian property of factorizations by nilradicals and Jacobson radical. The ring theoretical structures are investigated for various sorts of such factor rings which occur in the process.


Article Details

Supporting Agencies

This study was supported by the R$\&$E Program of Pusan Science High School in 2016.

References

[1] S.A. Amitsur, Radicals of polynomial rings, Canad. J. Math. 8 (1956), 355–361. Google Scholar

[2] D. Anderson, V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), 2265–2272. Google Scholar

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

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

[5] G.F. Birkenmeier, J.Y. Kim, J.K. Park, A connection between weak regularity and the simplicity of prime factor rings, Proc. Amer. Math. Soc. 122 (1994), 53–58. Google Scholar

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

[7] K.R. Goodearl and R.B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, Cambridge-New York-Port Chester-Melbourne-Sydney, 1989. Google Scholar

[8] J. Han, H.K. Kim, Y. Lee, Armendariz property over prime radicals, J. Korean Math. Soc. 50 (2013), 973–989. Google Scholar

[9] Y. Hirano, D.V. Huynh and J.K. Park, On rings whose prime radical contains all nilpotent elements of index two, Arch. Math. 66 (1996), 360–365. Google Scholar

[10] 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

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

[12] S.U. Hwang, Y.C. Jeon and Y. Lee, Structure and topological conditions of NI rings, J. Algebra 302 (2006), 186–199. Google Scholar

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

[14] N.K. Kim, K.H. Lee, Y. Lee, Power series rings satisfying a zero divisor property, Comm. Algebra 34 (2006), 2205–2218. Google Scholar

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

[16] T.K. Kwak, Y. Lee, A.C ̧. O ̈zcan, On Jacobson and nil radicals related to poly- nomial rings, J. Korean Math. Soc. 53 (2016), 415–431. Google Scholar

[17] T.Y. Lam, Lectures on Modules and Rings, Springer-Verlag, New York, 1991. Google Scholar

[18] J. Lambek, Lectures on Rings and Modules, Blaisdell Publishing Company, Waltham-Massachusetts-Toronto-London, 1966. Google Scholar

[19] C. Lanski, Nil subrings of Goldie rings are nilpotent, Canad. J . Math. 21 (1969), 904–907. Google Scholar

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