✦ LIBER ✦

Cohen–Macaulay Properties of Ring Homomorphisms

✍ Scribed by Luchezar L. Avramov; Hans-Bjørn Foxby

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 454 KB
Volume: 133
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1997.1684

No coin nor oath required. For personal study only.

✦ Synopsis

Numerical invariants which measure the Cohen Macaulay character of homomorphisms .: R Ä S of noetherian rings are introduced and studied. Comprehensive results are obtained for homomorphisms which are locally of finite flat dimension. They provide a point of view from which a variety of phenomena receive a unified treatment. The conceptual clarification and technical versatility of this approach leads, among other things, to a determination of those homomorphisms which preserve the Cohen Macaulay character of the rings, to the discovery of new classes of homomorphisms with remarkable stability properties, and to solutions of some problems on flat homomorphisms, raised by Grothendieck.

📜 SIMILAR VOLUMES

Quasi Cohen–Macaulay Properties of Local

Quasi Cohen–Macaulay Properties of Local Homomorphisms

✍ Anders Frankild 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 181 KB

For a large class of local homomorphisms : R ª S, including those of finite w Ž . G-dimension studied by Avramov and Foxby Proc. London Math. Soc. 75 1997 , x 241᎐270 , we assign a new numerical invariant called the quasi Cohen᎐Macaulay defect of , and a local homomorphism is called quasi Cohen᎐Maca

On the Cohen–Macaulay Property of Modula

On the Cohen–Macaulay Property of Modular Invariant Rings

✍ Gregor Kemper 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 203 KB

If V is a faithful module for a finite group G over a field of characteristic p, then the ring of invariants need not be Cohen᎐Macaulay if p divides the order of G. In this article the cohomology of G is used to study the question of Cohen᎐Macaulayness of the invariant ring. One of the results is a

Non-commutative Cohen–Macaulay Rings

✍ Wolfgang Rump 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 214 KB

## dedicated to professor klaus w. roggenkamp on the occasion of his 60th birthday We introduce a concept of Cohen-Macaulayness for left noetherian semilocal rings (and their modules) which generalizes the corresponding notion of commutative algebra and naturally applies to orders.

On Cohen–Macaulay Rings of Invariants

✍ M Lorenz; J Pathak 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 148 KB

We investigate the transfer of the Cohen᎐Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group action. As an illustration, we discuss the special case of mul

Cohen–Macaulay Rings Associated with Dig

Cohen–Macaulay Rings Associated with Digraphs

✍ Kazufumi Eto 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 171 KB

Let G be a digraph, that is, a pair of sets consisting of a set of vertices Ž . and a set of directed edges for a more precise definition, see Section 3 . It is an interesting problem to know how to count the Hamilton cycles of G, that is, cycles containing all vertices of G. In this paper, we will

Local Rings of Finite Cohen–Macaulay Typ

Local Rings of Finite Cohen–Macaulay Type

✍ Roger Wiegand 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 191 KB

Let R, m be a local Cohen᎐Macaulay ring whose m-adic completion R has an isolated singularity. We verify the following conjecture of F.-O. Schreyer: R has finite Cohen᎐Macaulay type if and only if R has finite Cohen᎐Macaulay type. We ww xx Ž . also show that the hypersurface k x , . . . , x r f has