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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2012, Issue 667


Connected sums of Gorenstein local rings

H. Ananthnarayan / Luchezar L. Avramov / W. Frank Moore
Published Online: 2011-08-28 | DOI: https://doi.org/10.1515/CRELLE.2011.132


Given surjective homomorphisms R → T ← S of local rings, and ideals in R and S that are isomorphic to some T-module V, the connected sum RTS is defined to be the ring obtained by factoring out the diagonal image of V in the fiber product R ×TS. When T is Cohen–Macaulay of dimension d and V is a canonical module of T, it is proved that if R and S are Gorenstein of dimension d, then so is RTS. This result is used to study how closely an artinian ring can be approximated by a Gorenstein ring mapping onto it. When T is regular, it is shown that RTS almost never is a complete intersection ring. The proof uses a presentation of the cohomology algebra as an amalgam of the algebras and over isomorphic polynomial subalgebras generated by one element of degree 2.

About the article

Received: 2010-05-07

Revised: 2010-12-20

Published Online: 2011-08-28

Published in Print: 2012-06-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2012, Issue 667, Pages 149–176, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2011.132.

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