Progress in commutative algebra

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This second volume of a two-part collection features state-of-the-art survey articles stemming from commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting. The articles explore various areas of commutative algebra, bridging Noetherian and non-Noetherian concepts. Key topics include non-Noetherian rings—covering factorization, ideal theory, and integrality—and Noetherian rings, focusing on local theory, graded situations, and their interplay with combinatorics and geometry. This volume specifically addresses closure operations, finiteness conditions, and factorization. It includes a comprehensive guide to closure operations by Epstein, alongside contributions from Schwede and Tucker on test ideals, and Enescu, who examines the Frobenius action on finite-dimensional vector spaces, all linked to tight closure. Finiteness properties of rings and modules are prevalent throughout commutative algebra, with non-Noetherian rings often exhibiting a finite number of prime ideals. Papers by Boynton and Sather-Wagstaff, as well as Watkins, delve into rings with finite Krull dimension and their extensions. Glaz and Schwarz discuss finiteness in commutative group rings, while Olberding presents constructions of rings with non-finitely generated integral closures. The final three papers investigate factorization broadly, including a study of the prime ideals of the projective line over integers by