𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Projective dimension is a lattice invariant

✍ Scribed by Barbara L. Osofsky

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
132 KB
Volume
161
Category
Article
ISSN
0022-4049

No coin nor oath required. For personal study only.

✦ Synopsis

We show that, for a free abelian group G and prime power p , every direct sum decomposition of the group G=p G lifts to a direct sum decomposition of G. This is the key result we use to show that, for R a commutative von Neumann regular ring, and E a set of idempotents in R, then the projective dimension of the ideal ER as an R-module the same as the projective dimension of the ideal EB as a B-module, where B is the boolean algebra generated by E βˆͺ {1}. This answers a 30 year old open question of R. Wiegand.

πŸ“œ SIMILAR VOLUMES

The Projective Noether Maple Package: Co
The Projective Noether Maple Package: Computing the Dimension of a Projective Variety
✍ Marc Giusti; Klemens HΓ€gele; GrΓ©goire Lecerf; JoΓ«l Marchand; Bruno Salvy πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 359 KB

Recent theoretical advances in elimination theory use straight-line programs as a data structure to represent multivariate polynomials. We present here the Projective Noether Package which is a Maple implementation of one of these new algorithms, yielding as a byproduct a computation of the dimensio

A projective invariant generalization of
A projective invariant generalization of the de Casteljau algorithm
✍ J. BenΓ­tez πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 404 KB

## a b s t r a c t A projective invariant generalization of the de Casteljau algorithm is described by using the cross ratio and an auxiliary line. We describe the implicit form of the section conics obtained by the algorithm proposed in this paper. Finally, we show how to construct specific conic