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Quasi-socle ideals and Goto numbers of parameters |
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| Authors: | Shiro Goto Satoru Kimura |
| Affiliation: | a Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan b Department of Information Technology and Applied Mathematics, Ton Duc Thang University, 98 Ngo Tat To Street, Ward 19, Binh Thanh District, Ho Chi Minh City, Viet Nam c Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, 10307 Hanoi, Viet Nam |
| Abstract: | Goto numbers  for certain parameter ideals Q in a Noetherian local ring (A,m) with Gorenstein associated graded ring  are explored. As an application, the structure of quasi-socle ideals I=Q:mq (q≥1) in a one-dimensional local complete intersection and the question of when the graded rings  are Cohen-Macaulay are studied in the case where the ideals I are integral over Q. |
| Keywords: | 13H10 13A30 13B22 13H15 |
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