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Cohen-Macaulay local rings with e2 = e1 − e + 1.
- Source :
-
Journal of Algebra . Dec2022, Vol. 611, p94-109. 16p. - Publication Year :
- 2022
-
Abstract
- In this paper we study Cohen-Macaulay local rings of dimension d , multiplicity e and second Hilbert coefficient e 2 in the case e 2 = e 1 − e + 1. Let h = μ (m) − d. If e 2 ≠ 0 then in our case we can prove that type (A) ≥ e − h − 1. If type (A) = e − h − 1 then we show that the associated graded ring G (A) is Cohen-Macaulay. In the next case when type (A) = e − h we determine all possible Hilbert series of A. In this case we show that depth G (A) completely determines the Hilbert Series of A. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 611
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 159189542
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2022.07.037