Commutative Algebra and its Applications: Proceedings of the Fifth International Fez Conference on Commutative Algebra and Applications, Fez, Morocco, June 23–28, 2008Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson 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. |
Contents
1 | |
9 | |
21 | |
Prüferlike conditions in pullbacks | 41 |
On propinquity of numerical semigroups and onedimensional local Cohen Macaulay rings | 49 |
nperfectness in pullbacks | 61 |
On flatness of factor rings and Krull dimension of tensor products | 69 |
Bouviers conjecture | 79 |
Integral basis of cubic number fields | 213 |
Some new approaches to integervalued polynomial rings | 223 |
vordering sequences and countable sets | 239 |
Mixed invertibility and Prüferlike monoids and domains | 247 |
Chain conditions in rings of the form A + XBX and A + XIX | 259 |
On n dperfect rings | 275 |
tclass semigroups of Noetherian domains | 283 |
Gorenstein dimensions in trivial ring extensions | 291 |
Elastic properties of some semirings defined by positive systems | 89 |
Integervalued polynomial in valued fields with an application to discrete dynamical systems | 103 |
Almost clean rings and arithmetical rings | 135 |
Amalgamated algebras along an ideal | 155 |
A sheaftheoretic bound on the cardinality of a finite ring | 173 |
Straight rings II | 183 |
On TVdomains | 207 |
Note on Prüfer multiplication domains and class groups | 301 |
Schubert varieties with inequidimensional singular locus | 313 |
On Matlis domains and Prüfer sections of Noetherian domains | 321 |
Transfinite selfidealization and commutative rings of triangular matrices | 333 |
Bass numbers and semidualizing complexes | 349 |
Every numerical semigroup is one over d of infinitely many symmetric numerical semigroups | 383 |
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Common terms and phrases
Algebra arithmetical ring assertion Assume canonical commutative ring contains Corollary Dedekind domain denote discrete divided domain divisorial DŒX dualizing element equivalent Example exists fact finite finitely generated ideal flat Gorenstein projective Hence homologically idempotent ifand implies infinite injective Int.D integer-valued polynomial integral domain integrally closed irreducible isomorphic Jaffard KŒX Krull dimension Krull domain Laskerian Lemma Math matrix maximal ideal modules monoid Mori domain Mori ring multiplicative n-perfect Nil.R Noetherian domain Noetherian ring nonnil nonzero numerical semigroup polynomial rings positive integer prime morphism principal ideal Proof Proposition 2.1 prove Prüfer domain Prüfer ring pSpecR pullback Pure Appl quasilocal quotient field R-complex R-module Recall resp result RHomR ring homomorphism satisfies Section semidualizing R-complex semidualizing R-module semigroup sequence Spec.A straight domain subring subset t-ideal t-regular Theorem 2.1 TV-domain v-ordering valuation domain weakly Matlis domain XB[X