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.
Publisher
Cambridge University Press (CUP)
Reference4 articles.
1. Algebras of cohomologically finite dimension
2. Theory of Rings;Jacobson;Amer. Math. Soc,1943
Cited by
177 articles.
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