Titlebook: Algebraic, Number Theoretic, and Topological Aspects of Ring Theory; Jean-Luc Chabert,Marco Fontana,Keith Johnson Book 2023 Springer Natur

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https://doi.org/10.1007/978-3-8349-8297-1Let . ⊆ . be a (unitary) extension of commutative rings. In this paper, we study several generalizations of the integral closure of . in . by replacing monic polynomials in .[.] with other subsets of .[.].

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Assessing Demobilization: Conceptual IssuesThis paper surveys recent works which investigate reductions and core of ideals in various settings of integral domains, including Prüfer domains, Noetherian domains, and pullback constructions. Results are presented and discussed without proofs, and examples are provided with full details from the original papers.

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https://doi.org/10.1057/9781403920072This work will present a method for constructing homogeneous integer-valued polynomials .∕. with . a product products of linear factors, with . a prime and . large relative to the degree of .. This is accomplished by connecting this problem to the older geometric problem of finding coverings of generalized projective planes by families of lines.

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Polynomial Root Extensions,Let . ⊆ . be a (unitary) extension of commutative rings. In this paper, we study several generalizations of the integral closure of . in . by replacing monic polynomials in .[.] with other subsets of .[.].

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