Higher derivations and automorphisms of complete local rings

Higher Derivations and Automorphisms of Complete Local Rings by Nickolas Heerema

This paper begins with a review of those aspects of the theory of higher derivations on fields which form a background for the study of recent uses of higher derivations in automorphism theory of complete local rings. Basic definitions and basic properties of convergent higher derivations on complete local rings are discussed including the concept of convergent rate group of automorphisms, the ...

Convergent Higher Derivations on Local Rings

Local higher derivations on C*-algebras are higher derivations

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

Higher derivations on rings and modules

Let τ be a hereditary torsion theory on ModR and suppose that Qτ : ModR → ModR is the localization functor. It is shown that for all R-modules M, every higher derivation defined on M can be extended uniquely to a higher derivation defined on Qτ(M) if and only if τ is a higher differential torsion theory. It is also shown that if τ is a TTF theory and Cτ : M →M is the colocalization functor, the...

Centralizing automorphisms and Jordan left derivations on σ-prime rings

Let R be a 2-torsion free σ-prime ring. It is shown here that if U 6⊂ Z(R) is a σ-Lie ideal of R and a, b in R such that aUb = σ(a)Ub = 0, then either a = 0 or b = 0. This result is then applied to study the relationship between the structure of R and certain automorphisms on R. To end this paper, we describe additive maps d : R −→ R such that d(u) = 2ud(u) where u ∈ U, a nonzero σ-square close...