• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 4,  2008, pp.545-551
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.4.545
Title & Authors

Abstract
Necessary and sufficient conditions for a radical class of rings to satisfy the polynomial equation $\small{\rho}$(R[x]) = ($\small{\rho}$(R))[x] have been investigated. The interrelationsh of polynomial equation, Amitsur property and polynomial extensibility is given. It has been shown that complete analogy of R.E. Propes result for radicals of matrix rings is not possible for polynomial rings.
Keywords
Language
English
Cited by
1.
ON -LIKE RADICALS OF RINGS, Bulletin of the Australian Mathematical Society, 2013, 88, 02, 331
2.
ON α-LIKE RADICALS, Bulletin of the Australian Mathematical Society, 2011, 1
References
1.
S. A. Amitsur, A general theory of radicals II, radicals in rings and bicategories, Amer. J. Math., 76(1954), 100-125.

2.
M. Aslam and A. M. Zaidi, Matrix equation in radicals, Stud. Sci. Math. Hung., 28(1993), 447-452.

3.
K. I. Beidar, E. R. Puczylowski and R. Wiegandt, Radicals and polynomial rings, J. Austral. Math. Soc., 72(2002), 23-31.

4.
D. M. Burton, A first course in rings and ideals, Addison-Wesley, 1970.

5.
N. J. Divinsky, Rings and radicals, University of British Columbia, Vancouver, 1965.

6.
B. J. Gardner, A note on radicals and polynomial rings, Math. Scand., 31(1972), 83-88.

7.
J. Krempa, On the properties of polynomial rings, Bull. Acad. Sci., 20(1972), 545-548.

8.
A. G. Kurosh, Radicals of rings and algebra, (Russian) Math. Sbornik N.S., 33(75), 13-26 (Translated in Rings, Modules and radicals, Proc. Colloq. Keozthely, 1297-1314, 1917) MR 15 # 194g.

9.
D. M. Olson, A uniformly strongly prime radical, J. Austral. Math. Soc., 43(1987), 95-102.

10.
R. E. Propes, The Radical equation ${\rho}(R_n)\;=\;({\rho}(R))_n$, Proc. Edin. Math. Soc., 14(1975), 257-259.

11.
L. H. Rowen, Ring theory (Vol.1), Academic Press Inc., 1988.

12.
A. Smoktunowicz, Polynomial rings over nil rings need not be nil, J. Algebra, 233(2000), 427-436.

13.
F. A. Szasz, Radical of rings, Mathematical Institute, Hungarian Academy of Sciences, 1981.

14.
S. Tumurbat and R. Wiegandt, Radicals of polynomial rings, Soochow J. Math., 29(2003) 425-434.

15.
R. Wiegandt, Radicals and semisimple classes of rings, Queen papers in pure and Appl. Math. 37, Kingston, Ontario, 1974.