The Veronesean subrings of Gorenstein rings

Subrings of zero-dimensional rings

When Sarah Glaz, Bill Heinzer and the junior author of this article approached Robert with the idea of editing a book dedicated to his work, we asked him to give us a list of his work and to comment on it to the extent he felt comfortable. As usual, he was extremely thorough in his response. When the authors of this article began to consider what topic we wanted to write about, we were impresse...

Gorenstein rings through face rings of manifolds

The face ring of a homology manifold (without boundary) modulo a generic system of parameters is studied. Its socle is computed and it is verified that a particular quotient of this ring is Gorenstein. This fact is used to prove that the sphere g-conjecture implies all enumerative consequences of its far reaching generalization (due to Kalai) to manifolds. A special case of Kalai’s manifold g-c...

Cohen-Macaulay and Gorenstein properties of invariant subrings

Subrings in Trigonometric Polynomial Rings

In this study we explore the subrings in trigonometric polynomial rings. Consider the rings T and T ′ of real and complex trigonometric polynomials over the fields R and its algebraic extension C respectively ( see [6]). We construct the subrings T0 of T and T ′ 0, T ′ 1 of T ′. Then T0 is a BFD whereas T ′ 0 and T ′ 1 are Euclidean domains. We also discuss among these rings the Condition : Let...

On the ubiquity of Gorenstein rings

Introduction APIARY [23~, and subsequently GORENSTEIN Eg] and SAMUEL [2(r proved 9 3-~ t that if (2 is a point on a plane curve then no=2d Q, where dQ=dlmw0/ 9 Q and nQ = dim C'Q/~Q, 9 being the local ring of Q, CQ its normalization, and ~Q the conductor. This condition has received attention from a variety of algebraic geometers, and recently ROQUETTE [19J and BEI~GER [52 have put it i n a rat...