Abelian property concerning factorization modulo radicals

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.

Keywords


idempotent, Abelian ring, factor ring, lower nilradical, upper nilradical, Jacobson radical.

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References


S.A. Amitsur, Radicals of polynomial rings, Canad. J. Math. 8 (1956), 355–361.

D. Anderson, V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), 2265–2272.

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

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

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.

K.R. Goodearl, Von Neumann Regular Rings, Pitman, London, 1979.

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.

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

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.

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

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

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

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

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

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

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.

T.Y. Lam, Lectures on Modules and Rings, Springer-Verlag, New York, 1991.

J. Lambek, Lectures on Rings and Modules, Blaisdell Publishing Company, Waltham-Massachusetts-Toronto-London, 1966.

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

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




DOI: http://dx.doi.org/10.11568/kjm.2016.24.4.737

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ISSN: 1976-8605 (Print), 2288-1433 (Online)

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