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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The Quadratic Tree of a Two-Dimensional Regular Local Ring,In this survey article, we discuss recent work describing the integrally closed rings between a two-dimensional regular local ring . and its quotient field .. A main emphasis is on those rings that can be obtained as an intersection of regular local rings between . and ..

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Reductions and Core of Ideals in Integral Domains: Some Recent Developments,This 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/10.1007/978-3-031-28847-0commutative rings; non-commutative rings; ring theory; integer-valued polynomials; rings and polynomials

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978-3-031-28849-4Springer Nature Switzerland AG 2023

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Victor H. Baryakhtar,Theo Rosendorfer(Commun Alg 14:557–580, 1986) systematized the construction, useful for finding interesting examples of rings with zero-divisors. We study three properties in the context of .?+?. rings, all relating to the prime spectrum (and ultimately the frame of radical ideals) of a commutative ring ..

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NATO Science Partnership Subseries: 1ipal ideals or possess the bounded factorization property. Along the way, we consider when a generalized power series ring is domainlike or (weakly) présimplifiable. As corollaries to our general theorems, we derive new factorization-theoretic results about (Laurent) power series rings and the “l(fā)arge polynomial rings” of Halter-Koch.