By Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson

This quantity comprises chosen refereed papers in line with lectures provided on the Â´;Fifth foreign Fez convention on Commutative Algebra and ApplicationsÂ´ that was once held in Fez, Morocco in June 2008. the quantity represents new traits and parts of classical study in the box, with contributions from many alternative international locations. moreover, the quantity has as a distinct concentration the learn and effect of Alain Bouvier on commutative algebra over the last thirty years.

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Then R is a -Noetherian ring. 4]). R/ D 1 and R has infinitely many maximal ideals. C/K 2 H is a -Noetherian ring with Krull dimension one which is not a Noetherian ring. C/Q is a -Noetherian ring with Krull dimension one which is not a Noetherian ring (where Z is the set of all integer numbers with quotient field Q). 5]). Let R be a Noetherian domain with quotient field K and Krull dimension n 2. C/K 2 H is a -Noetherian ring with Krull dimension n which is not a Noetherian ring. C/K is a -Noetherian ring with Krull dimension n which is not a Noetherian ring.

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11] A. Badawi, On Nonnil-Noetherian rings, Comm. Algebra 31 (2003), 1669–1677. [12] A. Badawi, Factoring nonnil ideals as a product of prime and invertible ideals, Bull. London Math. Soc. 37 (2005), 665–672. [13] A. Badawi, D. F Anderson and D. E. Dobbs, Pseudo-valuation Rings, Lecture Notes Pure Appl. Math. 185, pp. 57–67, Marcel Dekker, New York/Basel, 1997. [14] A. Badawi and D. E. Dobbs, Strong ring extensions and -pseudo-valuation rings, Houston J. Math. 32 (2006), 379–398. [15] A. Badawi and A.