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Reviewed by Ramdorai Sujatha References 1. A. Dress, C. Siebeneicher, The Burnside ring of the infinite cyclic group and its relation to the

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Classification of the ring of Witt vectors and the necklace ring associated with the formal group law X + Y − qXY. (English summary) J. Algebra 310 (2007), no. 1, 325–350. Let Fq(X, Y) = X + Y − qXY denote the one-dimensional formal group law, where q is any integer. This gives rise to the the q-deformation Witt vector functor W q from the category of rings to itself. In this paper, the author deals with the classification of W q (A) up to strict isomorphism, as q varies over the set of integers and A is a commutative ring. Associated to this study are the q-deformations of the necklace ring, denoted Nr q (A) and the q-deformations of the Grothendieck ring of formal power series, denoted Λ q (A). The author studies the relations between the q-deformed objects such as W q (A), Nr q (A) and Λ q (A). The particular case when A is the ring of integers gives rise to generalizations of product decompositions of formal power series. Another application is a q-analogue of the classical cyclotomic identity

Year: 2013
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