On \(\lambda\)-rings and topological realization
type: Item
instance of: scholarly article
title: On \(\lambda\)-rings and topological realization
zbMATH Open document ID: 1139.55012
DOI: 10.1155/IJMMS/2006/91267
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2007-06-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0501515
full work available at URL: https://eudml.org/doc/54257
review text: 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.
Mathematics Subject Classification ID: 55S25
Mathematics Subject Classification ID: 19L20
Mathematics Subject Classification ID: 55N15
zbMATH DE Number: 5164264
zbMATH Keywords: \(\lambda\)-ring
zbMATH Keywords: topological K-theory
author: Donald Yau
reviewed by: Do Ngoc Diep
MaRDI profile type: Publication
arXiv ID: math/0501515
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OpenAlex ID: W2088897420
description: scientific article