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- W2003634824 abstract "In 1977 Buchsbaum and Eisenbud gave a complete characterization of grade 3 perfect ideals I of type 1 (i.e., Gorenstein), in a noetherian local ring R . Exploiting the fact that a minimal free resolution for R/I has a structure of associative, commutative, differential graded algebra they also studied successfully the structure of grade 3 almost complete intersections ideals. In 1981 and 1982 Kustin and Miller studied the structure of Gorenstein ideals of grade 4, but they introduced a new variable to the problem. They defined the concept of defect of an ideal and they found that for grade 4 Gorenstein ideals, the structures vary, in part, according to the value of d ( I ), the defect of I . Later in 1984, Ann Brown in her Ph.D. thesis gave a structure theorem for grade 3 perfect ideals of type 2 and defect positive. She also proved that for grade 3 perfect ideals of type 2, d ( I ) can be either 0 or 1. The purpose of this paper is to give a structure theorem for grade 3 perfect ideals of type 3 and defect 2 or greater. Furthermore, this structure theorem permits us to establish that for grade 3, type 3 perfect ideals, d ( I ) can be either 0 or 1 or 2 or 4." @default.
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- W2003634824 date "1989-06-01" @default.
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- W2003634824 title "A structure theorem for type 3, grade 3 perfect ideals" @default.
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- W2003634824 doi "https://doi.org/10.1016/0021-8693(89)90047-1" @default.
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