A β\beta-ring is a commutative ring, RR, equipped with a set of operations, β H:RR\beta_H: R \to R, indexed by subgroups of symmetric groups, S nS_n, satisfying a number of conditions. They may be seen as collections of integral linear combinations of generalized symmetric powers defined on Burnside rings. The cohomotopy of a space, π 0(X)\pi^0(X), is a β\beta-ring (Guillot 06, Thrm 4.5).

They are completely unrelated to relational beta-modules.


Note that there are variations in the literature as to the definition of β\beta-rings. For a close comparison with λ-rings, see

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