2 citations · 4 across the 9 of their papers we have counts for
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The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two
Bruce Olberding, William Heinzer
Let be a normal Noetherian local domain of Krull dimension two. We examine intersections of rank one discrete valuation rings that birationally dominate . We restrict to the…
Radical factorization in finitary ideal systems
Bruce Olberding, Andreas Reinhart
In this paper we investigate the concept of radical factorization with respect to finitary ideal systems of cancellative monoids. We present new characterizations for r-almost Dede…
Radical factorization in commutative rings, monoids and multiplicative lattices
Bruce Olberding, Andreas Reinhart
In this paper we study the concept of radical factorization in the context of abstract ideal theory in order to obtain a unified approach to the theory of factorization into radica…
Krull's Principal Ideal Theorem in non-Noetherian settings
Bruce Olberding
Let be a finitely generated ideal of a commutative ring . Krull's Principal Ideal Theorem states that if is Noetherian and is minimal over a principal ideal of ,…
The tree of quadratic transforms of a regular local ring of dimension two
William Heinzer, K. Alan Loper, Bruce Olberding
Let be a 2-dimensional regular local ring and let denote the quadratic tree of 2-dimensional regular local overrings of . We explore the topology of the tree a…
De-noetherizing Cohen-Macaulay rings
Laszlo Fuchs, Bruce Olberding
We introduce a new class of commutative {non-noetherian} rings, called -subperfect rings, generalizing the almost perfect rings that have been studied recently by Fuchs-Salce. F…