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

Abstract

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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 .

How to cite

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Ananthnarayan, 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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  1. Ananthnarayan, H., Approximating Artinian Rings by Gorenstein Rings and Three-Standardness of the Maximal Ideal, Ph.D. Thesis, University of Kansas (2009). (2009) 
  2. Ananthnarayan, H., Avramov, L. L., Moore, W. F., 10.1515/CRELLE.2011.132, J. Reine Angew. Math. 667 (2012), 149-176. (2012) Zbl1271.13047MR2929675DOI10.1515/CRELLE.2011.132
  3. Ananthnarayan, H., Celikbas, E., Laxmi, J., Yang, Z., 10.1016/j.jalgebra.2019.01.036, J. Algebra 527 (2019), 241-263. (2019) Zbl1410.13014MR3924433DOI10.1016/j.jalgebra.2019.01.036
  4. Avramov, L. L., Kustin, A. R., Miller, M., 10.1016/0021-8693(88)90056-7, J. Algebra 118 (1988), 162-204. (1988) Zbl0648.13008MR0961334DOI10.1016/0021-8693(88)90056-7
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  10. Levin, G. L., Avramov, L. L., 10.1016/0021-8693(78)90191-6, J. Algebra 55 (1978), 74-83. (1978) Zbl0407.13018MR0515760DOI10.1016/0021-8693(78)90191-6
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