Abstract
Let R be a ring with 1. All modules considered are to be unital left R-modules unless otherwise noted.Definition. A σ-set for R is a nonempty set Σ of left ideals of R satisfying the following conditions:(σ1)If I ∊ Σ, J is a left ideal of I, and J ⊇ I, then J ∊ Σ.(σ2)If I ∊ Σ and r ∊ R, then Ir-1 = {s ∊ R | sr ∊ I} ∊ Σ.(σ3)If I is a left ideal of R, J ∊ Σ, and It-1 ∊ Σ for each t ∊ J, then I ∊ Σ.
Publisher
Canadian Mathematical Society
Cited by
6 articles.
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