Parametric decomposition of powers of ideals versus regularity of sequences

Let be an ideal in a Noetherian local ring . Then the sequence is -regular if every is a non-zerodivisor in and if for all integers , where runs over the elements of the set .

     

Artificial nucleosides possessing metal binding sites at the 3'- and 5'-positions of the deoxyribose moieties

This paper describes a convenient synthetic procedure for nucleoside mimics, 1-6, in which the 3',5'-hydroxy groups of natural 2'-deoxythymidine or 2'-deoxyadenosine are replaced by thiol, amine, or alkylthiol groups. Such nucleosides would be built up into a single DNA strand with cooperative participation of metal coordination, where internucleoside linkages are replaced by metal complexation motifs. The X-ray crystal structure and complexation behaviors of 3',5'-dithiothymidine, 1, with Au(I) are also reported.     

Unprecedented hydrothermal reaction of o-phenylaniline and related derivatives with cyclic ketones. A novel approach to the construction of phenanthridine and quinoline ring systems

[reaction: see text] A new method for synthesizing phenanthridine and its related compounds was developed using the condensation of o-phenylaniline and its homologues with cyclic ketones under hydrothermal conditions.     

Good ideals in Gorenstein local rings

Let be an -primary ideal in a Gorenstein local ring (, ) with , and assume that contains a parameter ideal in as a reduction. We say that is a good ideal in if is a Gorenstein ring with . The associated graded ring of is a Gorenstein ring with if and only if . Hence good ideals in our sense are good ones next to the parameter ideals in . A basic theory of good ideals is developed in this paper. We have that is a good ideal in if and only if and . First a criterion for finite-dimensional Gorenstein graded algebras over fields to have nonempty sets of good ideals will be given. Second in the case where we will give a correspondence theorem between the set and the set of certain overrings of . A characterization of good ideals in the case where will be given in terms of the goodness in their powers. Thanks to Kato's Riemann-Roch theorem, we are able to classify the good ideals in two-dimensional Gorenstein rational local rings. As a conclusion we will show that the structure of the set of good ideals in heavily depends on . The set may be empty if , while is necessarily infinite if and contains a field. To analyze this phenomenon we shall explore monomial good ideals in the polynomial ring in three variables over a field . Examples are given to illustrate the theorems.

     

Finite Modules of Finite Injective Dimension Over a Noetherian Algebra

Let R be a commutative Noetherian ring. Let P(R) (respectively,I(R)) be the category of all finite R-modules of finite projective(respectively, injective) dimension. Sharp [9] constructed acategory equivalence between I(R) and P(R) for certain Cohen–Macaulaylocal rings R. Thus many properties about finite modules offinite projective dimension can be connected with those of finiteinjective dimension through this equivalence.