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Quadratic Gorenstein rings and the Koszul property I.
- Source :
-
Transactions of the American Mathematical Society . Feb2021, Vol. 374 Issue 2, p1077-1093. 17p. - Publication Year :
- 2021
-
Abstract
- Let R be a standard graded Gorenstein algebra over a field presented by quadrics. In [Compositio Math. 129 (2001), no. 1, 95-121], Conca-Rossi-Valla show that such a ring is Koszul if reg R ≤ 2 or if reg R = 3 and c = codim R ≤ 4, and they ask whether this is true for reg R = 3 in general. We determine sufficient conditions on a non-Koszul quadratic Cohen-Macaulay ring R that guarantee the Nagata idealization ~ R = R × ωR(−a−1) is a non-Koszul quadratic Gorenstein ring. We prove there exist rings of regularity 3 satisfying our conditions for all c ≥ 9; this yields a negative answer to the question from the above-mentioned paper. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GORENSTEIN rings
*COHEN-Macaulay rings
*KOSZUL algebras
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 374
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 147993472
- Full Text :
- https://doi.org/10.1090/tran/8214