Modules satisfying ACC on a certain type of colons

Chin-pi Lu

Vol. 131 (1988), No. 2, 303–318

DOI: 10.2140/pjm.1988.131.303

Abstract

Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the form N : B ⊆ N : B² ⊆ N : B³ ⊆⋯ for every submodule N of M and every finitely generated ideal B of R. We investigate the class of such modules M and show that various important properties of Noetherian modules and rings can be generalized to modules and rings of this class.

Mathematical Subject Classification 2000

Primary: 13E05

Secondary: 13J10

Milestones

Received: 23 September 1986

Published: 1 February 1988