J. Austral. Math. Soc.
72 (2002), 2331

Radicals and polynomial rings



and

R. Wiegandt
Institute of Mathematics
Hungarian Academy of Sciences
Budapest
Hungary
wiegandt@mathinst.hu



Abstract

We prove that polynomial rings in one
indeterminate over nil rings are antiregular
radical and uniformly strongly prime radical.
These give some approximations of Kothe's
problem. We also study the uniformly strongly
prime and superprime radicals of polynomial rings
in noncommuting indeterminates. Moreover, we
show that the semiuniformly strongly prime
radical coincides with the uniformly strongly
prime radical and that the class of
semisuperprime rings is closed under taking
finite subdirect sums.

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