Výsledky vyhledávání - "Raymond C. Heitmann"

Autor: Raymond C. Heitmann

Publikováno v: Journal of Pure and Applied Algebra. 226:106809

It is shown that if ( R , m , k ) is a complete local domain with char k = p > 0 and R + is its integral closure in an algebraic closure of the quotient field, then both the m -adic and p-adic completions of R + are integral domains. More generally,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::df1c12f830a40b9b74bbcec30145499b
https://doi.org/10.1016/j.jpaa.2021.106809

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Integral closures of Noetherian domains

Autor: Raymond C. Heitmann

Publikováno v: Journal of Pure and Applied Algebra. 221:1999-2009

It has long been known that an integral domain A can be Noetherian while its integral closure A ′ is not. However, when Heinzer asked whether A ′ can have an infinitely generated maximal ideal, the question went unanswered. In this article, a loc

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::229cd94a6868f1fe387323c6ffed82a1
https://doi.org/10.1016/j.jpaa.2016.10.014

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Big Cohen-Macaulay algebras and the vanishing conjecture for maps of Tor in mixed characteristic

Autor: Raymond C. Heitmann, Linquan Ma

Publikováno v: Algebra Number Theory 12, no. 7 (2018), 1659-1674

We prove a version of weakly functorial big Cohen-Macaulay algebras that suffices to establish Hochster-Huneke's vanishing conjecture for maps of Tor in mixed characteristic. As a corollary, we prove an analog of Boutot's theorem that direct summands

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Extended plus closure in complete local rings

Autor: Raymond C. Heitmann, Linquan Ma

The (full) extended plus closure was developed as a replacement for tight closure in mixed characteristic rings. Here it is shown by adapting Andr\'{e}'s perfectoid algebra techniques that, for complete local rings that have F-finite residue fields,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::635ff213e33a89385fe6b0ef9dcc0f51

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Are complete intersections complete intersections?

Autor: David A. Jorgensen, Raymond C. Heitmann

Publikováno v: Journal of Algebra. 371:276-299

A commutative local ring is generally defined to be a complete intersection if its completion is isomorphic to the quotient of a regular local ring by an ideal generated by a regular sequence. It has not previously been determined whether or not such

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7907f2f5d8f293c35cab3c6c12d731a3
https://doi.org/10.1016/j.jalgebra.2012.08.006

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Tight closure in non-excellent rings

Autor: Raymond C. Heitmann

Publikováno v: Journal of Algebra. 324(3):430-441

Some examples are constructed to demonstrate that tight closure need not satisfy several key properties when the ring is not excellent. In particular, there are counterexamples to colon-capturing and persistence. A consequence is that R + need not be

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Realizing infinite cardinal numbers via maximal chains of intermediate fields

Autor: Raymond C. Heitmann, David E. Dobbs

Publikováno v: Rocky Mountain J. Math. 44, no. 5 (2014), 1471-1503

For each nonzero cardinal number $\kappa$, there is a field extension $\mathbf{Q} \subseteq L$ and a maximal chain $\mathcal{H}_{\kappa}$ of intermediate fields going from $\mathbf{Q}$ to $L$ such that the cardinal number of $\mathcal{H}_{\kappa}$ is

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a8bef1d28e13bf5d4b312eb8adbd1b46
http://projecteuclid.org/euclid.rmjm/1420071551

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