Bounds on Annihilator Lengths in Families of Quotients of Noetherian Rings

✍ Scribed by C.A. Yackel

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 205 KB
• Volume: 228
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8317

✦ Synopsis

In this paper we study lengths of annihilators of m-primary ideals, J, in quotients Ž . of finitely generated modules, M, over local rings, R, m , modulo m-primary ideals generated by a sequence of ring elements each raised to a power, I s N Ž N N . f , . . . , f , as a function of this power. The motivation for studying these lengths 1 s arose initially from tight closure theory. However, the function we define to organize this study is closely related to the Hilbert᎐Kunz and Hilbert᎐Samuel functions. Using new observations on the implications of the structure of complete local rings and subsequent homological algebra results, we give an upper bound, a constant times N dy 2 , for the length of Ann J when the dimension of M is M r I M N d.