Etale Extensions of Λ-rings
نویسنده
چکیده
Given a λ-ring A and a formally etale morphism f : A→ B of commutative rings, one may ask: What are the possible λ-ring strutures on B such that f is a map of λ-rings? We give the answer: Such a lifted λ-ring structure on B is determined uniquely by a compatible choice of lifts of the Adams operations ψ from A to B for all primes p which satisfy Frobenius congruences. In other words, to extend a λ-ring structure along a formally etale morphism, we need not be concerned about the “non-linear” part of the λ-ring structures in question.
منابع مشابه
Extensions of strongly alpha-reversible rings
We introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. We firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. We next argue about the strong$alpha$-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown ...
متن کاملOre extensions of skew $pi$-Armendariz rings
For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...
متن کاملOn derivations and biderivations of trivial extensions and triangular matrix rings
Triangular matrix rings are examples of trivial extensions. In this article we determine the structure of derivations and biderivations of the trivial extensions, and thereby we describe the derivations and biderivations of the upper triangular matrix rings. Some related results are also obtained.
متن کامل