λ-ring (Rev #1, changes)

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A commutative ring $K$ is called a **$\lambda$-ring** if we are given a family of set operations $\lambda^k \colon K \to K$ for $k \geq 0$ such that for all $x,y \in K$

- $\lambda^0(x) = 1$ and $\lambda^1(x) = x$
- $\lambda^k(x+y) = \sum_{i=0}^k \lambda^i(x) \lambda^{k-i}(y).

Note: there is a group homomorphism $\lambda_t$ from the additive group of $K$ to the multiplicative group $W(K) = 1+tK[[t]]$

A **special $\lambda$-ring** is a $\lambda$-ring $K$ such that the group homomorphism $\lambda_t \colon K \to W(K)$ is a $\lambda$-ring homomorphism.

- Charles A. Weibel, The $K$-book: An introduction to algebraic $K$-theory, American Mathematical Society, Graduate Studies in Mathematics Volume 145, 2013.

category: mathematical methods