Progress in commutative algebra

Autor*innen

• Timothy B. P. Clark

Parameter

• Mathematik

Mehr zum Buch

This collection is the first of two volumes stemming from commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting. It explores diverse areas of commutative algebra, bridging Noetherian and non-Noetherian aspects. The volumes highlight current trends in two active areas: non-Noetherian rings (factorization, ideal theory, integrality) and Noetherian rings (local theory, graded situations, interactions with combinatorics and geometry). This volume features combinatorial and homological surveys. The combinatorial papers reflect the growing emphasis on the interplay between algebra and combinatorics, using combinatorial techniques to investigate algebraic structures, as seen in the works of Fløystad, Geramita, Harbourne, Migliore, Cooper, Clark, and Mermin. Additionally, algebraic invariants are employed to analyze combinatorial structures like graphs and simplicial complexes, exemplified by Morey and Villarreal's work on edge ideals. Homological techniques have become essential for studying Noetherian rings, fostering interactions with fields such as algebraic topology, analysis, and combinatorics. The homological articles included illustrate how these techniques enhance our understanding of both Noetherian and non-Noetherian rings and singularities, as demonstrated in the contributions by Roberts, Yao, Hummel, and Leuschke.

• Sprache: Englisch
• Erscheinungsdatum: 2012