646 research outputs found
Generalized Burnside-Grothendieck ring functor and aperiodic ring functor associated with profinite groups
For every profinite group , we construct two covariant functors
and from the category of commutative rings with
identity to itself, and show that indeed they are equivalent to the functor
introduced in [A. Dress and C. Siebeneicher, The Burnside ring of
profinite groups and the Witt vectors construction, {\it Adv. in Math.}
{\bf{70}} (1988), 87-132]. We call the generalized
Burnside-Grothendieck ring functor and the aperiodic
ring functor (associated with ). In case is abelian, we also construct
another functor from the category of commutative rings with
identity to itself as a generalization of the functor introduced in
[K. Varadarajan, K. Wehrhahn, Aperiodic rings, necklace rings, and Witt
vectors, {\it Adv. in Math.} {\bf 81} (1990), 1-29]. Finally it is shown that
there exist -analogues of these functors (i.e, , and ) in case the profinite
completion of the multiplicative infinite cyclic group.Comment: minor corrections, 35 page
Necklace rings and logarithmic functions
In this paper, we develop the theory of the necklace ring and the logarithmic
function. Regarding the necklace ring, we introduce the necklace ring functor
from the category of special \ld-rings into the category of special
\ld-rings and then study the associated Adams operators. As far as the
logarithmic function is concerned, we generalize the results in Bryant's paper
(J. Algebra. 253 (2002); no.1, 167-188) to the case of graded Lie
(super)algebras with a group action by applying the Euler-Poincar\'e principle
q-Deformed necklace rings and q-Möbius function
AbstractWe introduce a q-deformation of the classical Möbius function and investigate its properties in connection with q-deformed truncated necklace rings. Also, we study the strictly natural isomorphism of q-deformed necklace rings
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