Homological Properties of Powers of the Maximal Ideal of a Local Ring

By Liana Sega. 2001

49 citations recorded by the source corpus.

Abstract It is known that the powers m n of the maximal ideal of a local Noetherian ring share certain homological properties for all sufficiently large integers n . For example, the natural homomorphisms R  →  R / m n are Golod, respectively, small, for all large n . We give effective bounds on the smallest integers n for which such properties begin to hold.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f0c8ad49edb6cce83842fb63f5471d2332259029

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In Algebra and Number Theory

1. Bogdan Gheorghe
2. M. Rossi
3. Zhouli Xu
4. Guozhen Wang
5. E. D. Negri
6. Aldo Conca

In Geometry and Topology

1. M. Rossi
2. Bogdan Gheorghe
3. Zhouli Xu
4. Aldo Conca
5. E. D. Negri
6. Guozhen Wang

Citations in the corpus

• The special fiber of the motivic deformation of the stable homotopy category is algebraic (2018, background): “9 are well known (see [66], for example).”
• Koszul Algebras and Regularity (2012, background): “M.When ldR(M)<∞we say that in the minimal free resolution the linear part predominates. Koszul modules have appeared previously in the literature under the name “modules with linear resolution” in [Se] and “weakly Koszul” in [MVZ] . KOSZUL ALGEBRAS AND REGULARITY 23 By definition R is Koszul as an”