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http://dx.doi.org/10.4134/JKMS.2016.53.2.415

ON JACOBSON AND NIL RADICALS RELATED TO POLYNOMIAL RINGS  

Kwak, Tai Keun (Department of Mathematics Daejin University)
Lee, Yang (Department of Mathematics Education Pusan National University)
Ozcan, A. Cigdem (Department of Mathematics Hacettepe University)
Publication Information
Journal of the Korean Mathematical Society / v.53, no.2, 2016 , pp. 415-431 More about this Journal
Abstract
This note is concerned with examining nilradicals and Jacobson radicals of polynomial rings when related factor rings are Armendariz. Especially we elaborate upon a well-known structural property of Armendariz rings, bringing into focus the Armendariz property of factor rings by Jacobson radicals. We show that J(R[x]) = J(R)[x] if and only if J(R) is nil when a given ring R is Armendariz, where J(A) means the Jacobson radical of a ring A. A ring will be called feckly Armendariz if the factor ring by the Jacobson radical is an Armendariz ring. It is shown that the polynomial ring over an Armendariz ring is feckly Armendariz, in spite of Armendariz rings being not feckly Armendariz in general. It is also shown that the feckly Armendariz property does not go up to polynomial rings.
Keywords
feckly Armendariz ring; Jacobson radical; nilradical; polynomial ring; Armendariz ring;
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Times Cited By KSCI : 2  (Citation Analysis)
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