A characterization of cominimax and weakly cofinite modules. Issue 12 (1st December 2020)

• Record Type: Journal Article
• Authors: Aghapournahr, Moharram; Bahmanpour, Kamal
• Is Part Of: Communications in algebra. Volume 48:Issue 12(2020)
• Page Start: 5421
• Page End: 5429
• Publication Date: 2020-12-01
• Subjects: Cofinite module -- cominimax module -- weakly cofinite module -- weakly Laskerian moduleminimax module; 13E05 -- 13D07; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1789988
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let R be a commutative Noetherian ring and I be an ideal of R . Let M be an arbitrary R -module. In this paper we establish some results concerning the cofiniteness properties of modules. It is shown that, M is I -cominimax if and only if there is an ideal J ⊇ I with dim R / J ≤ 0 such that M is ( I, V ( J ) ) -cofinite and the R -module Ext R i ( R / J, M ) is finitely generated, for each i ≥ 0 . Moreover, it is shown that M is I -weakly cofinite if and only if there is an ideal J ⊇ I such that V ( J ) is a finite set and M is ( I, V ( J ) ) -cofinite.