Integral derivations

Derivations and the Integral Closure of Ideals

Let (R, m) be a complete local domain containing the rationals. Then there exists an integer l such that for any ideal I ⊆ R, if f ∈ m, f / ∈ In, then there exists a derivation δ of R with δ(f) / ∈ In+l. This note grew out of a question raised by C. Huneke some years ago: Suppose (R, m) is a complete local domain with perfect residue class field k which it contains. Call an element x ∈ R deriva...

Path integral derivations of novel complex trajectory methods

Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path integral, but taking into account the h̄ dependence of both the amplitude and the phase of the intial wave function, thus giving rise to the need for complex clas...

Zero Derivations

In LI 31.2, J. Rubach proposes a modified version of OT that features derivations. In the present article I argue that, while some modification to the original formulation by Prince and Smolensky is needed, the correct one is not to re-introduce derivations, but rather to take fuller advantage of OT’s inherent parallelism. I propose that outputs must be related not only to inputs, but to other,...

Derivations and skew derivations of the Grassmann algebras

Surprisingly, skew derivations rather than ordinary derivations are more basic (important) object in study of the Grassmann algebras. Let Λn = K⌊x1, . . . , xn⌋ be the Grassmann algebra over a commutative ring K with 12 ∈ K, and δ be a skew K-derivation of Λn. It is proved that δ is a unique sum δ = δ ev + δ of an even and odd skew derivation. Explicit formulae are given for δ and δ via the ele...

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras