Ideal Theoretic Methods in Commutative Algebra

Preface, Contributors, 1. F-Rational Rings and the Integral Closures of Ideals II, 2. Cancellation Modules and Related Modules, 3. Abstract Ideal Theory from Krull to the Present, 4. Conditions Equivalent to Seminormality in Certain Classes of Commutative Rings, 5. The Zero-Divisor Graph of a Commutative Ring, II, 6. Some Examples of Locally Divided Rings, 7. On the Dimension of the Jacquet Module of a Certain Induced Representation, 8. m-Canonical Ideals in Integral Domains II, 9. The t- and v-Spectra of the Ring of Integer-Valued Polynomials Over a Valuation Domain, 10. Weakly Factorial Rings with Zero Divisors, 11. Equivalence Classes of Minimal Zero-Sequences Modulo a Prime, 12. Towards a Criterion for Isomorphisms of Complexes, 13. Ideals Having a One-Dimensional Fiber Cone, 14. Recent Progress on Going-Down II, 15. Kronecker Function Rings: A General Approach, 16. On the Complete Integral Closure of the Rees Algebra, 17. A New Criterion for Embeddability in a Zero-Dimensional Commutative Ring, 18. Finite Conductor Properties of R(X) and R, 19. Building Noetherian and Non-Noetherian Integral Domains Using Power Series, 20. Integrality Properties in Rings with Zero Divisors, 21. Prime-Producing Cubic Polynomials, 22. Stability of Ideals and Its Applications, 23. Categorically Domains: Highlighting the (Domain) Work of James A. Huckaba, Index

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• Álgebra

Semistar Operation;ideal theory;Kronecker Function Ring;commutative rings;Divided Prime Ideal;commutative algebra;Unique Minimal Prime Ideal;cancellation modules;Nonmaximal Prime Ideal;rational rings;Minimal Prime Ideal;Infinite Residue Field;Integral Domain;Maximal Ideal;Krull Domains;Total Quotient Ring;Dedekind Domain;Noetherian Local Ring;Commutative Ring;Cancellation Ideal;Local Cohen Macaulay Ring;Noetherian Ring;Quotient Field;Regular Ideal;Bezout Domain;Prime Ideal;Completely Integrally Closed;Noetherian Domains;Regular Element;Principal Ideal