A Note on the Λ-structure on the Burnside Ring
نویسنده
چکیده
Let G be a finite group and let S be a G-set. The Burnside ring of G has a natural structure of a λ-ring, {λn}n∈N. However, a priori λ (S) can only be computed recursively, by first computing λ(S), . . . , λ(S). In this paper we establish an explicit formula, expressing λ(S) as a linear combination of classes of G-sets.
منابع مشابه
A Note on the Λ-structure on the Burnside Ring
Let G be a finite group and let S be a G-set. The Burnside ring of G has a natural structure of a λ-ring, {λ}n∈N. However, a priori λn(S), where S is a G-set, can only be computed recursively, by first computing λ1(S), . . . , λn−1(S). In this paper we establish an explicit formula, expressing λn(S) as a linear combination of classes of G-sets.
متن کاملGreen functors, crossed G-monoids, and Hochschild constructions
Let G be a finite group, and R be a commutative ring. This note proposes a generalization to any Green functor for G over R of the construction of the Hochschild cohomology ring HH∗(G,R) from the ordinary cohomology functor H∗(−, R). Another special case is the construction of the crossed Burnside ring of G from the ordinary Burnside functor. The general abstract setting is the following : let ...
متن کاملThe slice Burnside ring and the section Burnside ring of a finite group
This paper introduces two new Burnside rings for a finite group G, called the slice Burnside ring and the section Burnside ring. They are built as Grothendieck rings of the category of morphisms of G-sets, and of Galois morphisms of G-sets, respectively. The well known results on the usual Burnside ring, concerning ghost maps, primitive idempotents, and description of the prime spectrum, are ex...
متن کاملA note on a graph related to the comaximal ideal graph of a commutative ring
The rings considered in this article are commutative with identity which admit at least two maximal ideals. This article is inspired by the work done on the comaximal ideal graph of a commutative ring. Let R be a ring. We associate an undirected graph to R denoted by mathcal{G}(R), whose vertex set is the set of all proper ideals I of R such that Inotsubseteq J(R), where J(R) is...
متن کاملA note on the socle of certain types of f-rings
For any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. The condition is that every minimal ideal of the ring consist entirely of bounded elements. It is not too stringent, and is satisfied, for instance, by rings of ...
متن کامل