On Andrunakievich's chain and Koethe's problem
Resource
Israel Journal of Mathematics, 180(1), 119-128
Journal
Israel Journal of Mathematics
Journal Volume
180
Journal Issue
1
Pages
119-128
Date Issued
2010
Date
2010
Author(s)
Chebotar, M.A.
Lee, P-H
Puczylowski, E.R.
Abstract
In 1969 Andrunakievich asked whether one gets a ring without nonzero nil left ideals from an arbitrary ring R by factoring out the ideal A(R) which is the sum of all nil left ideals of R. Recently, it was shown that this problem is equivalent to Koethe's problem. In this context one may consider the chain of ideals, which starts with A1 (R)=A(R) ⊆ A2(R), where A2(R)/A1 (R) = A(R/A1 (R)), and extends by repeating this process. We study the properties of this chain and show that, assuming a negative solution of Koethe's problem, this chain can terminate at any given ordinal number.
Type
journal article
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