Commutative algebra and its applications

✍ Scribed by Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding

• Publisher: de Gruyter
• Year: 2009
• Tongue: English
• Leaves: 394
• Series: De Gruyter Proceedings in Mathematics
• Category: Library

✦ Synopsis

This volume contains selected refereed papers based on lectures presented at the ´;Fifth International Fez Conference on Commutative Algebra and Applications´ that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.

✦ Table of Contents

Frontmatter
......Page 1
Table of contents......Page 7
Splitting sets and weakly Matlis domains......Page 9
Divisibility properties in ultrapowers of commutative rings......Page 17
On rings with divided nil ideal: a survey......Page 29
Prüfer-like conditions in pullbacks......Page 49
On propinquity of numerical semigroups and one-dimensional local Cohen Macaulay rings......Page 57
n-perfectness in pullbacks......Page 69
On flatness of factor rings and Krull dimension of tensor products......Page 77
Bouvier’s conjecture......Page 87
Elastic properties of some semirings defined by positive systems......Page 97
Integer-valued polynomial in valued fields with an application to discrete dynamical systems......Page 111
Almost clean rings and arithmetical rings......Page 143
Amalgamated algebras along an ideal......Page 163
A sheaf-theoretic bound on the cardinality of a finite ring......Page 181
Straight rings, II......Page 191
On TV-domains......Page 215
Integral basis of cubic number fields......Page 221
Some new approaches to integer-valued polynomial rings......Page 231
v-ordering sequences and countable sets......Page 247
Mixed invertibility and Prüfer-like monoids and domains......Page 255
Chain conditions in rings of the form A + XB[X] and A + XI[X]......Page 267
On (n, d)-perfect rings......Page 283
t-class semigroups of Noetherian domains......Page 291
Gorenstein dimensions in trivial ring extensions......Page 299
Note on Prüfer *-multiplication domains and class groups......Page 309
Schubert varieties with inequidimensional singular locus......Page 321
On Matlis domains and Prüfer sections of Noetherian domains......Page 329
Transfinite self-idealization and commutative rings of triangular matrices......Page 341
Bass numbers and semidualizing complexes......Page 357
Every numerical semigroup is one over d of infinitely many symmetric numerical semigroups......Page 391