On the Dimension of Modules and Algebras (III): Global Dimension
Author:
- 1 October 1955
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 9, 67-77
Abstract
Let Λ be a ring with unit. If A is a left Λ-module, the dimension of A (notation: 1.dimΛA) is defined to be the least integer n for which there exists an exact sequence0 → Xn → … → X0 → A → 0where the left Λ-modules X0, …, Xn are projective. If no such sequence exists for any n, then 1. dimAA = ∞. The left global dimension of Λ is1. gl. dim Λ = sup 1. dimAAwhere A ranges over all left Λ-modules, The condition 1. dimA A < n is equivalent with (A, C) = 0 for all left Λ-modules C. The condition 1.gl. dim Λ < n is equivalent with = 0. Similar definitions and theorems hold for right Λ-modules.Keywords
This publication has 1 reference indexed in Scilit:
- Algebras of cohomologically finite dimensionCommentarii Mathematici Helvetici, 1954