Multiplicative ideal theory of noncommutative Krull pairs. I: Module systems, Krull ring-type chain conditions, and application to two-sided ideals
نویسندگان
چکیده
منابع مشابه
Order ideals and a generalized Krull height theorem
Let N be a finitely generated module over a Noetherian local ring (R,m). We give criteria for the height of the order ideal N∗(x) of an element x ∈ N to be bounded by the rank of N . The Generalized Principal Ideal Theorem of Bruns, Eisenbud and Evans says that this inequality always holds if x ∈ mN . We show that the inequality even holds if the hypothesis becomes true after first extending sc...
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Introduction and summary. In the theory of non-commutative rings certain distinguished subrings, one-sided and two-sided ideals, play the important roles. Ideals combine under crosscut, union and multiplication and hence are an instance of a lattice over which a non-commutative multiplication is defined.f The investigation of such lattices was begun by W. Krull (Krull [3]) who discussed decompo...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1977
ISSN: 0021-8693
DOI: 10.1016/0021-8693(77)90299-x