Commutative Algebra and its Applications (eBook)

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Marco Fontana, Università degli Studi “Roma Tre”, Rome, Italy; Salah-Eddine Kabbaj, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia; Bruce Olberding, New Mexico State University, Las Cruces, USA; Irena Swanson, Reed College, Portland, USA.

Frontmatter 2
Table of contents 8
Splitting sets and weakly Matlis domains 10
Divisibility properties in ultrapowers of commutative rings 18
On rings with divided nil ideal: a survey 30
Prüfer-like conditions in pullbacks 50
On propinquity of numerical semigroups and one-dimensional local Cohen Macaulay rings 58
n-perfectness in pullbacks 70
On flatness of factor rings and Krull dimension of tensor products 78
Bouvier’s conjecture 88
Elastic properties of some semirings defined by positive systems 98
Integer-valued polynomial in valued fields with an application to discrete dynamical systems 112
Almost clean rings and arithmetical rings 144
Amalgamated algebras along an ideal 164
A sheaf-theoretic bound on the cardinality of a finite ring 182
Straight rings, II 192
On TV-domains 216
Integral basis of cubic number fields 222
Some new approaches to integer-valued polynomial rings 232
v-ordering sequences and countable sets 248
Mixed invertibility and Prüfer-like monoids and domains 256
Chain conditions in rings of the form A + XB[X] and A + XI[X] 268
On (n, d)-perfect rings 284
t-class semigroups of Noetherian domains 292
Gorenstein dimensions in trivial ring extensions 300
Note on Prüfer *-multiplication domains and class groups 310
Schubert varieties with inequidimensional singular locus 322
On Matlis domains and Prüfer sections of Noetherian domains 330
Transfinite self-idealization and commutative rings of triangular matrices 342
Bass numbers and semidualizing complexes 358
Every numerical semigroup is one over d of infinitely many symmetric numerical semigroups 392