For every profinite group G, we construct two covariant functors ∆G and APG from the category of commutative rings with identity to itself, and show that indeed they are equivalent to the functor WG introduced in [A. Dress and C. Siebeneicher, The Burnside ring of profinite groups and the Witt vectors construction, Adv. Math. 70 (1988), 87-132]. We call ∆G the generalized Burnside-Grothendieck ...

The aim of this article is to give a self-contained account the algebra and model theory Cohen rings, natural generalization Witt rings. rings are only valuation in case residue field perfect, arise as ring analogon over imperfect fields. Just one studies truncated understand we study positive characteristic well zero. Our main results relative completeness result for which imply corresponding ...

In this paper, we construct a q-deformation of the Witt-Burnside ring of a profinite group over a commutative ring, where q ranges over the ring of integers. When q = 1, this coincides with the Witt-Burnside ring introduced by A. Dress and C. Siebeneicher (Adv. Math. 70 (1988), 87-132). To achieve our goal we first show that there exists a q-deformation of the necklace ring of a profinite group...

In this paper, we give a formula as an exponential sum for a homogeneous weight defined by Constantinescu and Heise [3] in the case of Galois rings (or equivalently, rings of Witt vectors) and use this formula to estimate the weight of codes obtained from algebraic geometric codes over rings.