Non-Noetherian Commutative Ring Theory / Edition 1

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This volume consists of twenty-one articles by many of the most prominent researchers in non-Noetherian commutative ring theory. The articles combine in various degrees surveys of past results, recent results that have never before seen print, open problems, and an extensive bibliography. One hundred open problems supplied by the authors have been collected in the volume's concluding chapter. The entire collection provides a comprehensive survey of the development of the field over the last ten years and points to future directions of research in the area.
Audience: Researchers and graduate students; the volume is an appropriate source of material for several semester-long graduate-level seminars and courses.

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Table of Contents

Preface. 1. GCD Domains, Gauss' Lemma, and Contents of Polynomials; D.D. Anderson. 2. The Class Group and Local Glass Group of an Integral Domain; D.F. Anderson. 3. Mori Domains; V. Barucci. 4. What's New About Integer-Valued Polynomials on a Subset? P.-J. Cahen, J.-L. Chabert. 5. Half-Factorial Domains, a Survey; S.T. Chapman, J. Coykendall. 6. On Generalized Lengths of Factorizations in Dedekind and Krull Domains; S.T. Chapman, et al. 7. Recent Progress on Going-Down I; D.E. Dobbs. 8. Localizing Systems and Semistar Operations; M. Fontana, J.A. Huckaba. 9. Ideal Theory in Pullbacks; S. Gabelli, E. Houston. 10. Commutative Rings of Dimension 0; R. Gilmer. 11. Finite Conductor Rings with Zero Divisors; S. Glaz. 12. Construction of Ideal Systems with Nice Noetherian Properties; F. Halter-Koch. 13. Generalized Local Rings and Finite Generation of Powers of Ideals; W. Heinzer, M. Roitman. 14. Connecting Trace Properties; J.A. Huckaba, I. Papick. 15. Constructing Examples of Integral Domains by Intersecting Valuation Domains; K.A. Loper. 16. Examples Built with D+M, A+XB[X] and Other Pullback Constructions; T.G. Lucas. 17. T-Closedness; G. Picavet, M. Picavet-L'Hermitte. 18. E-rings and Related Structures; C. Vinsonhaler. 19. Prime Ideals and Decompositions of Modules; R. Wiegand, S. Wiegand. 20. Putting t-Invertibility to Use; M. Zafrullah. 21. One Hundred Problems in Commutative Ring Theory; S.T. Chapman, S. Glaz. Index.
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