Titlebook: Rings, Polynomials, and Modules; Marco Fontana,Sophie Frisch,Paolo Zanardo Book 2017 Springer International Publishing AG 2017 Gaussian pr

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,Divisorial Prime Ideals in Prüfer Domains, domain ., then . is divisorial as an ideal of . but . = .. is not divisorial as an ideal of ... We review several relevant results on divisorial primes and present some new sufficient conditions on when . is divisorial as an ideal of ., and if not when a . exists such that . = . ∩ . is divisorial as an ideal of ..

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,Minimal Generating Sets for the ,-Algebra Int(,, ,), are not always able to extract from a generating set a minimal one. In particular, we prove that, in local fields, the generating set of integer-valued polynomials obtained by de Shalit and Iceland by means of Lubin-Tate formal group laws is minimal. In our proofs we make an extensive use of Bhargava’s notion of .-ordering.

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d are not yet well represented in book form.In addition to r.This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems t

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,-Absorbing Ideals of Commutative Rings and Recent Progress on Three Conjectures: A Survey, more general concept than 2-absorbing ideals is the concept of .-absorbing ideals. Let . ≥ 1 be a positive integer. A proper ideal . of . is called an . of . if .., .., ., .. ∈ . and ....⋯.. ∈ ., then there are . of the ..’s whose product is in .. The concept of .-absorbing ideals is a generalizati

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Embedding Dimension and Codimension of Tensor Products of Algebras over a Field,s of .-algebras. We use results and techniques from prime spectra and dimension theory to establish an analogue of the “special chain theorem” for the embedding dimension of tensor products, with effective consequence on the transfer or defect of regularity as exhibited by the (embedding) codimensio

羽毛长成

,Minimal Generating Sets for the ,-Algebra Int(,, ,),For instance, the binomial polynomials . where . is a prime number and . is any nonnegative integer, form a minimal generating set for the classical .-algebra Int. In the local case, when . is a valuation domain and . is a regular subset of ., we are able to construct minimal generating sets, but we