The Structure of Chains of Ulrich Ideals in Cohen-Macaulay Local Rings of Dimension One
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DOI: 10.1007/s40306-018-0283-y
Abstract: This paper studies Ulrich ideals in one-dimensional Cohen-Macaulay local rings. A correspondence between Ulrich ideals and overrings is given. Using the correspondence, chains of Ulrich ideals are closely explored. The specific cases where the rings… read more here.
Keywords: cohen macaulay; macaulay local; chains ulrich; structure chains ... See more keywords
Applications and homological properties of local rings with decomposable maximal ideals
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DOI: 10.1016/j.jpaa.2018.06.006
Abstract: We construct a local Cohen-Macaulay ring $R$ with a prime ideal $\mathfrak{p}\in\spec(R)$ such that $R$ satisfies the uniform Auslander condition (UAC), but the localization $R_{\mathfrak{p}}$ does not satisfy Auslander's condition (AC). Given any positive integer… read more here.
Keywords: mathfrak; homological properties; cohen macaulay; local rings ... See more keywords
On One-Dimensional Local Rings and Berger’s Conjecture
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DOI: 10.1017/s0013091523000214
Abstract: Let k be a field of characteristic zero and let $\Omega_{A/k}$ be the universally finite differential module of a k-algebra A, which is the local ring of a closed point of an algebraic or algebroid… read more here.
Keywords: dimensional local; berger; local rings; berger conjecture ... See more keywords
Completions of Countable Excellent Local Rings in Equal Characteristic Zero
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DOI: 10.1142/s0219498824501913
Abstract: We characterize which complete local (Noetherian) rings T containing the rationals are the completion of a countable excellent local ring S. We also discuss the possibilities for the map from the minimal prime ideals of… read more here.
Keywords: rings equal; equal characteristic; completions countable; local rings ... See more keywords