Titlebook: Non-Noetherian Commutative Ring Theory; Scott T. Chapman,Sarah Glaz Book 2000 Springer Science+Business Media Dordrecht 2000 Dimension.Div

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Recent Progress on Going-Down I,earlier history, Ira Papick and I wrote a survey [78] which appeared in 1978. Since then, work in this area has continued unabated, and I propose to survey most of the post-1977 work concerning “going-down.” Because of limitations of space, our focus here is almost exclusively on papers of which I w

Intellectual

Localizing Systems and Semistar Operations,of star operation, as developed in Gilmer’s book [12], and hence the related classical theory of ideal systems based on the works of W. Krull, E. Noether, H. Prüfer, and P. Lorenzen from the 1930’s. For a systematic treatment of these ideas, see the books by P. Jaffard [17] and F. Halter-Koch [14],

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Commutative Rings of Dimension 0, ., and hence is the unity of . All allusions to the dimension of a ring refer to its Krull dimension. Thus dim . = . if there exists a chain ...i. … < .. of proper prime ideals of ., but no longer such chain; dim . = ∞ if there exist arbitrarily long chains of prime ideals of . This paper is concer

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Finite Conductor Rings with Zero Divisors, prominence with the publication of McAdam’s work [35]. The definition of a finite conductor domain appears in an early unpublished version of McAdam’s manuscript, but it appears in print for the first time in [11]. The notion embodies, in its various aspects, both factoriality properties and finite

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Examples Built with D+M, A+XB[X] and other Pullback Constructions, of R. Gilmer’s book on multiplicative ideal theory [37] (or [38]). Others may have encountered them in Appendix 2 of the original Queen’s Notes version of the same book [36], or in A. Seidenberg’s second paper on the dimension of polynomial rings [53]. Basically in all three, the concentration is o