Type-sequences of modules

✍ Scribed by A. Oneto; E. Zatini

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 154 KB
• Volume: 160
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00070-0

✦ Synopsis

Let R be a complete and integral local k-algebra of dimension one, k an algebraically closed ÿeld of characteristic zero. In this paper the notion of type-sequence, given for rings in Barucci et al. (AMS Mem. 125 (598) (1997) Ch. II,1), is extended to any ÿnitely generated torsion-free R-module of rank 1. A module M , of Cohen-Macaulay type r1(M ); whose type-sequence is [r1(M ); 1; : : : ; 1] is said to have "minimal type-sequence", brie y m:t:s: The family of m:t:s: R-modules, which includes the canonical module, is described by means of value sets, the conductor c(M ), the -invariant (M ) and the C.M. type r1(M ). In the case of rings the m:t:s: property is called "almost Gorenstein" (see Barucci and Fr oberg, J.