ω-MODULES OVER COMMUTATIVE RINGS
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Let R be a commutative ring and let M be a GV -torsionfree R-module. Then M is said to be a w-module if Ext<수식> for any J ∈ GV (R), and the ω-envelope of M is defined by Mω = {x ∈E(M)ㅣJx ⊆ M for some J ∈ GV (R)}. In this paper, ω-modules over commutative rings are considered, and the theory of ω-operations is de-veloped for arbitrary commutative rings. As applications, we give some characterizations of ω-Noetherian rings and Krull rings.
Abstract
Let R be a commutative ring and let M be a GV -torsionfree R-module. Then M is said to be a w-module if Ext<수식> for any J ∈ GV (R), and the ω-envelope of M is defined by Mω = {x ∈E(M)ㅣJx ⊆ M for some J ∈ GV (R)}. In this paper, ω-modules over commutative rings are considered, and the theory of ω-operations is de-veloped for arbitrary commutative rings. As applications, we give some characterizations of ω-Noetherian rings and Krull rings.
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