# Associated graded rings and connected sums

H. Ananthnarayan; Ela Celikbas; Jai Laxmi; Zheng Yang

Czechoslovak Mathematical Journal (2020)

- Volume: 70, Issue: 1, page 261-279
- ISSN: 0011-4642

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topAnanthnarayan, H., et al. "Associated graded rings and connected sums." Czechoslovak Mathematical Journal 70.1 (2020): 261-279. <http://eudml.org/doc/297227>.

@article{Ananthnarayan2020,

abstract = {In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring $Q$, which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincaré series of $Q$.},

author = {Ananthnarayan, H., Celikbas, Ela, Laxmi, Jai, Yang, Zheng},

journal = {Czechoslovak Mathematical Journal},

keywords = {associated graded ring; fibre product; connected sum; short Gorenstein ring; stretched Gorenstein ring; Poincaré series},

language = {eng},

number = {1},

pages = {261-279},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Associated graded rings and connected sums},

url = {http://eudml.org/doc/297227},

volume = {70},

year = {2020},

}

TY - JOUR

AU - Ananthnarayan, H.

AU - Celikbas, Ela

AU - Laxmi, Jai

AU - Yang, Zheng

TI - Associated graded rings and connected sums

JO - Czechoslovak Mathematical Journal

PY - 2020

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 70

IS - 1

SP - 261

EP - 279

AB - In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring $Q$, which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincaré series of $Q$.

LA - eng

KW - associated graded ring; fibre product; connected sum; short Gorenstein ring; stretched Gorenstein ring; Poincaré series

UR - http://eudml.org/doc/297227

ER -

## References

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