On \(\lambda\)-rings and topological realization
A \(\lambda\)-ring is a commutative ring \(R\) with operations \(\lambda^i\), \(i\geq 0\) which act like the exterior power operations. If at the same time the ring \(R\) is filtered and the filtration ideals \(I^n\), \(R = I^0 \supset I^1 \supset \dots \), \(n \geq 0\) are closed under the \(\lambda\)-operations, one speaks of a filtered \(\lambda\)-ring. In the paper under review the author considers the question of classifying the \(\lambda\)-ring structure over power series and over the truncated polynomial series. It is shown that most possibly truncated power series rings admit uncountably many filtered \(\lambda\)-ring structures (Thm 1.1). The question how many of these \(\lambda\)-ring structures are topologically realizable by the K-theory of torsion-free spaces is also considered for truncated polynomial rings. The main classification results are stated in Theorem 1.3 and Theorem 1.6.
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