Groups Acting on Tensor Products

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be gained from an examination of the universal distributive products: tensor products. We give a detailed description of the groups preserving tensor products over semisimple and semiprimary rings, and present effective algorithms to construct generators for these groups. We also discuss applications of our methods to algorithmic problems for which all currently known methods require an exponential amount of work. (C) 2013 Elsevier B.V. All rights reserved.

A General Approach Towards the Synthesis of Amido-Functionalized Biodegradable Polyesters

The thesis presented here describes methodologies to produce pendant group functionalized polyesters from amido-functionalized α-hydroxy acids. The synthetic methods used to produce the functionalized α-hydroxy acids are compatible with a wide array of functional groups, making this technique highly versatile. The synthesis of functionalized polyesters was investigated to develop polymers with properties that may improve the capabilities of existing biodegradable polyesters for applications in controlled release pharmaceuticals. Chemically modified a-hydroxy acids were synthesized by reacting glyoxylic acid with a primary or secondary amide. To demonstrate the utility of this reaction, fourstructurally dissimilar amide substituents were examined including 2-pyrrolidione, benzamide, acetamide and acrylamide. The reaction is synthetically simple, provides high yields and is uniquely flexible, functionalized monomer. The compatibility of this procedure with the collection of functional groups mentioned circumvents the need for syntheses. The amido-functionalized monomers were polymerized by two different techniques: melt polycondensation and solution polymerization. Melt polycondensation was conducted by heating the monomer past its melting temperature under reduced pressure. Oligomeric functionalized polyesters (= 800 g/mol) with low PDIs (= 1.05) were obtained by melt polycondensation. Melt polycondensation was not compatible with all of the synthesized monomers. Two of the monomers (containing benzamide and acrylamide functionalities) degraded before the polycondensation reaction occurred. Thermal gravimetric analysis confirmed that a process other than polyesterification was occurring, indicating that some amido-functionalized α-hydroxy acids cannot be synthesized in the melt.Solution polymerization was conducted to polymerize functionalized α-hydroxy acids that were incompatible with melt polycondensation. Several modified Steglich polyesterifications were tested including p-toluenesulfonic acid mediated and scandium (III) triflate catalyzed. Only oligomeric functionalized polyesters were formed bythis method. A number of possible side reactions including the formation of an N-acylurea and a cyclic polymer ring were possible. The utility of this procedure appears to be limited due to the complexity of the reaction and its inability to produce high molecular weight polymer.