Growth of graded noetherian rings

We show that every graded locally finite right noetherian algebra has sub-exponential growth. As a consequence, every noetherian algebra with exponential growth has no finite dimensional filtration which leads to a right (or left) noetherian associated graded algebra. We also prove that every connected graded right noetherian algebra with finite global dimension has finite GK-dimension. Using this, we can classify all connected graded noetherian algebras of global dimension two.

     

Visible Light Mediated Aryl Migration by Homolytic C−N Cleavage of Aryl Amines

The photocatalytic preparation of aminoalkylated heteroarenes from haloalkylamides via a 1,4‐aryl migration from nitrogen to carbon, conceptually analogous to a radical Smiles rearrangement, is reported. This method enables the substitution of amino groups in heteroaromatic compounds with aminoalkyl motifs under mild, iridium(III)‐mediated photoredox conditions. It provides rapid access to thienoazepinone, a pharmacophore present in multiple drug candidates for potential treatment of different conditions, including inflammation and psychotic disorders.     

Algebras associated to elliptic curves

This paper completes the classification of Artin-Schelter regular algebras of global dimension three. For algebras generated by elements of degree one this has been achieved by Artin, Schelter, Tate and Van den Bergh. We are therefore concerned with algebras which are not generated in degree one. We show that there exist some exceptional algebras, each of which has geometric data consisting of an elliptic curve together with an automorphism, just as in the case where the algebras are assumed to be generated in degree one.

In particular, we study the elliptic algebras , , and , where , which were first defined in an earlier paper. We omit a set consisting of 11 specified points where the algebras become too degenerate to be regular. Theorem. Let represent , or , where . Then is an Artin-Schelter regular algebra of global dimension three. Moreover, is a Noetherian domain with the same Hilbert series as the (appropriately graded) commutative polynomial ring in three variables.

This, combined with our earlier results, completes the classification.

     

Sterically crowded cyclohexanes-2 synthesis,structure and dynamics of hexaspiro[2.0.3.0.2.0.3.0.2.0.3.0]heneicosane

The synthesis, structure and dynamics of hexaspiro[2.0.3.0.2.0.3.0.- 2.0.3.0]heneicosane $\text{3}$ are described. $\text{3}$ adopts a chair conformation in the crystal state but prefers a chair-to-twistboat equilibrium in solution. The activation parameters of the chair-to-chair interconversion of $\text{3}$ and the closely related hexaspiro[2.0.2.0.2.0.2.0.2.0.2.0]- octadecane ([6]rotane) $\text{4}$ have been determined by DNMR. Some consequences appertaining to the conformation and dynamics of other fully (cyclo-)alkylated cyclohexanes are discussed.     

Transition metal mediated asymmetric synthesis X. Homochiral π-complexes with planar chirality: synthetic equivalents of chiral cyclohexadiene dications

Homochiral 6-methoxy-substituted dienyltricarbonyliron complexes have been obtained from 1-methylcyclohexa-1,3-diene-5,6-diol (available via microbial oxidation of toluene) by complexation and removal of an allylic substituent with acids or with triphenylcarbenium tetrafluoroborate. A variety of optically active tricarbonyliron complexes have been produced from these compounds. The optical purity of the product and the stereochemistry of the complexation reaction have been determined. The high efficiency of chirality transfer during complexation of 5,6-dimethoxy-substituted dienes makes this method suitable as a general route to resolved organoiron complexes.