Totally ordered sets and the prime spectra of rings

Let T be a totally ordered set and let D(T) denotes the set of all cuts of T. We prove the existence of a discrete valuation domain O_v such that T is order isomorphic to two special subsets of Spec(O_v). We prove that if A is a ring (not necessarily commutative), whose prime spectrum is totally ordered and satisfies (K2), then there exists a totally ordered set U?Spec(A) such that the prime spectrum of A is order isomorphic to D(U). We also present equivalent conditions for a totally ordered set to be a Dedekind totally ordered set. At the end, we present an algebraic geometry point of view.     

Non-Catalyzed Reductions With Formate Salts: Conversion of Nitroaromatic Compounds to the Corresponding Primary Amines

One of the more important transformations in aromatic chemistry involves nitration of the ring followed by reduction¹ of the nitro group to the corresponding primary amine. Despite its low cost, ease of handling, and known² property of being a convenient hydrogen donor, formic acid (or formate salts, which are even more active hydride donors²) was not utilized for this reduction until recently when Heck and Cortese reported ³ the palladium-catalyzed reduction of nitroaromatics using triethylammonium formate. Since the latter reagent in N,N-dimethylformamide (DMF) had previously⁴ been shown to reduce the carbon-carbon double bond in good Michael acceptors without the presence of a metal catalyst, we decided to examine non-catalytic systems involving formic acid⁵ for effecting reduction of the nitro group.     

Doped Sol-Gel Materials as Heterogeneous Reagents for Organic Synthesis

We advance the use of reactive doped sol-gel materials as heterogeneous reagents for organic-chemistry synthesis. Three approaches were demonstrated with SiO₂-based materials: Direct physical entrapment of the organic reagent; in-situ generation of an inorganic reagent within the matrix; and covalent attachment of the reagent to the matrix. With the first, entrapped p-toluenesulfonic acid facilitated the 100% yield esterification of benzoic acid with 1-pentanol, and the 100% dehydration of 1-tetralol to 1,2-dihydronaphthalene; with the second approach, a sol-gel oxidant, SiO₂/MnO₂ was used to convert benzyl alcohol to benzaldehyde and 1-tetralol to 1-tetralone; and with the third, anchored propylamine facilitated dehydrobromination reactions resulting in double-bond formation. Several other reactions with these reagents are described, and their reactivities analyzed.