Chapter

Commutative Algebra

pp 353-375

Date:

Open Problems in Commutative Ring Theory

  • Paul-Jean CahenAffiliated with Email author 
  • , Marco FontanaAffiliated withDipartimento di Matematica e Fisica, Università degli Studi Roma Tre
  • , Sophie FrischAffiliated withMathematics Department, Graz University of Technology
  • , Sarah GlazAffiliated withDepartment of Mathematics, University of Connecticut

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Abstract

This chapter consists of a collection of open problems in commutative algebra. The collection covers a wide range of topics from both Noetherian and non-Noetherian ring theory and exhibits a variety of research approaches, including the use of homological algebra, ring theoretic methods, and star and semistar operation techniques. The problems were contributed by the authors and editors of this volume, as well as other researchers in the area.

Keywords

Prüfer ring Homological dimensions Integral closure Group ring Grade Complete ring McCoy ring Straight domain Divided domain Integer-valued polynomials Factorial Density Matrix ring Overring Absorbing ideal Kronecker function ring Stable ring Divisorial domain Mori domain Finite character PvMD Semistar operation Star operation Jaffard domain Locally tame domain Factorization Spectrum of a ring Integral closure of an ideal Rees algebra Rees valuation

Mathematics Subject Classification (2010):

13-02 13A05 13A15 13A18 13B22 13C15 13D05 13D99 13E05 13F05 13F20 13F30 13G05