Golodideale der gestalt a ∩ b

Herzog, Jürgen; Steurich, Manfred

doi:10.1016/0021-8693(79)90186-8

Cited by 14 publications

(10 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where p is place of the top non-vanishing homology of the Koszul homology. In the case that I and J are not necessarily monomial ideals, it is only known that R/IJ is Golod if IJ = I ∩ J, see [12].…”

Section: Introductionmentioning

confidence: 99%

Ordinary and symbolic powers are Golod

Herzog

Huneke

2013

Advances in Mathematics

Self Cite

View full text Add to dashboard Cite

Let S be a positively graded polynomial ring over a field of characteristic 0, and I ⊂ S a proper graded ideal. In this note it is shown that S/I is Golod if ∂(I) 2 ⊂ I. Here ∂(I) denotes the ideal generated by all the partial derivatives of elements of I. We apply this result to find large classes of Golod ideals, including powers, symbolic powers, and saturations of ideals.2000 Mathematics Subject Classification. 13A02, 13D40.

show abstract

Section: Introductionmentioning

confidence: 99%

Ordinary and symbolic powers are Golod

Herzog

Huneke

2013

Advances in Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Because the Stanley-Reisner ideal of (K * L) * is the product of those of K * and L * , this corollary provides a topological proof of a classical result given in [13]. The reader may also refer to [6] and [17].…”

Section: Resultsmentioning

confidence: 86%

“…We also thank Lukas Katthän for his comments on the first draft of this paper. He kindly pointed out the papers [13] and [6], and provided us with ideas for simplifying the arguments in the subsection 5.3. We would also like to thank the anonymous referee for his/her careful reading of our manuscript and his/her many constructive comments and suggestions, which helped us to improve the manuscript.…”

mentioning

confidence: 99%

A Golod complex with non-suspension moment-angle complex

Iriye

Yano

2017

Topology and its Applications

View full text Add to dashboard Cite

show abstract

“…Remark 4.5. Corollary 4.4 was already known by work of Herzog and Steurich (see [8]) showing that R/IJ is a Golod ring for I and J transverse. This, in particular, implies that the multiplication on the Tor-algebra is trivial.…”

Section: Koszul Homology For Products Of Transverse Idealsmentioning

confidence: 76%

Vanishing of Avramov Obstructions for Products of Sequentially Transverse Ideals

VandeBogert¹

2020

Preprint

View full text Add to dashboard Cite

Two ideals I and J are called transverse if I ∩ J = IJ. We show that the obstructions defined by Avramov for classes of (sequentially) transverse ideals in regular local rings are always 0. In particular, we compute an explicit free resolution and Koszul homology for all such ideals, also showing that the multiplication in the Tor-algebra is always trivial in positive homological degrees. We conclude with questions about the existence of associative multiplicative structures on the minimal free resolution of the quotient defined by products of transverse ideals.

show abstract

Golodideale der gestalt a ∩ b

Cited by 14 publications

References 5 publications

Ordinary and symbolic powers are Golod

Ordinary and symbolic powers are Golod

A Golod complex with non-suspension moment-angle complex

Vanishing of Avramov Obstructions for Products of Sequentially Transverse Ideals

Contact Info

Product

Resources

About