Continuous rings with chain conditions
نویسندگان
چکیده
منابع مشابه
Rings with Annihilator Chain Conditions and Right Distributive Rings
We prove that if a right distributive ring R, which has at least one completely prime ideal contained in the Jacobson radical, satisfies either a.c.c or d.c.c. on principal right annihilators, then the prime radical of R is the right singular ideal of R and is completely prime and nilpotent. These results generalize a theorem by Posner for right chain rings.
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In his article: “Untersuchungen über die Teilbarkeitseigenschaften in Körpern” J. Reine Angew. Math. 168, 1 36, 1932 [21], Heinz Prüfer introduced a new class of integral domains, namely those domains R in which all finitely generated ideals are invertible. He also proved that to verify this condition, it suffices to check that it holds for all two-generated ideals of R. This was the modest beg...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1994
ISSN: 0022-4049
DOI: 10.1016/0022-4049(94)00017-4