Amitsur cohomology of cubic extensions of algebraic integers

LetK be the rational fieldQ or a complex quadratic number field other than . LetL be a normal three-dimensional field extension onK. IfR andS are the rings of algebraic integers ofK andL respectively, then the Amitsur cohomology groupH ² (S/R, U) is trivial. Inflation and class numbers give information about cohomology arising from certain nonnormal cubic extensions. This work was supported in part by NSF Grant GP-28409.     

Real metal parameters of niobium from the attenuation of transverse ultrasonic waves

Measurements of the attenuation of shear waves in superconducting niobium along [100] for frequencies from 18 to 105 MHz show that the Fermi surface deformation parameter for shear strains is large.     

Straight Rings

A (commutative integral) domain is called a straight domain if A ? B is a prime morphism for each overring B of A; a (commutative unital) ring A is called a straight ring if A/P is a straight domain for all P ∈ Spec(A). A domain is a straight ring if and only if it is a straight domain. The class of straight rings sits properly between the class of locally divided rings and the class of going-down rings. An example is given of a two-dimensional going-down domain that is not a straight domain. The classes of straight rings, of locally divided rings, and of going-down rings coincide within the universe of seminormal weak Baer rings (for instance, seminormal domains). The class of straight rings is stable under formation of homomorphic images, rings of fractions, and direct limits. The “straight domain" property passes between domains having the same prime spectrum. Straight domains are characterized within the universe of conducive domains. If A is a domain with a nonzero ideal I and quotient field K, characterizations are given for A ? (I: _K I) to be a prime morphism. If A is a domain and P ∈ Spec(A) such that A _P is a valuation domain, then the CPI-extension C(P) := A + PA _P is a straight domain if and only if A/P is a straight domain. If A is a going-down domain and P ∈ Spec(A), characterizations are given for A ? C(P) to be a prime morphism. Consequences include divided domain-like behavior of arbitrary straight domains.     

Chemically induced electron spin polarization in electron-transfer reactions

Chemically induced electron polarization (CIDEP) has been observed for the durosemiquinone radical anion generated in the flash photolysis of solutions of duroquinone in the presence of various amines. The initial polarization has been measured directly by using a fast response time-resolved E.S.R. spectrometer. The magnitude of polarization is shown to depend on amine concentration and identity, and the solvent medium. Conventional nanosecond flash photolysis has been used to measure duroquinone triplet lifetimes under various conditions. The results are discussed in terms of the triplet mechanism and the radical pair mechanism.     

On Going Down For Simple Overrings II

This paper deals with two themes involving the going down (GD) behavior of the overrings of a domain R. First, as illustrated by several results in [3] and [4], hypotheses about GD often replace stronger assumptions about flatness or one-dimensionality in sets of conditions implying that R is Prüfer. Second, as shown by the two-dimensional example in [4]. Remarks (iii)], some sort of finiteness condition is required in conjunction with GD hypotheses in order for R to be Prüfer.     

A proof of the arithmetic-geometric mean inequality using non-Euclidean geometry

This note presents a proof of the arithmetic-geometric mean inequality that uses basic facts about the upper half-plane model of hyperbolic plane geometry. This material could find use as enrichment material in any model-oriented course on the classical geometries.     

Every Commutative Ring Has a Minimal Ring Extension

Let R be a commutative unital ring and E a unital R-module. Then the canonical injective ring homomorphism from R into the idealization R(+) E is a minimal ring homomorphism if and only if E is a simple R-module. For E nonzero, R(+)E is not (R-algebra isomorphic to) an overring of R. If E ₁ and E ₂ are nonisomorphic simple R-modules, then R(+) E ₁ and R(+) E ₂ give minimal ring extensions of R which are not isomorphic as R-algebras. The ring of dual numbers over R is a minimal ring extension of R ? R × R is a minimal ring extension of R ? R is a field.     

Transfer of Krull Dimension,Lying-Over,and Going-Down to the Fixed Ring

Let G be a group acting via ring automorphisms on a commutative unital ring R. If Spec(R) has no infinite antichains and either R a domain or G finitely generated, then R ^G  ? R has the lying-over property. If R is semiquasilocal and dim(R) = 0, then dim(R ^G ) = 0. If 1 ≤ d ≤ ∞, new examples are given such that d = dim(R) ≠ dim(R ^G ) < ∞. If G is locally finite on R, then R ^G  ? R satisfies universally going-down. Consequently, if G is locally finite, the S-domain, strong S-domain and universally strong S-domain properties descend from R to R ^G . If R is a domain, then G is locally finite on R ? R is integral over R ^G . One cannot delete the “domain” hypothesis.