Kaplansky-type Theorems, II
نویسندگان
چکیده
منابع مشابه
Kaplansky-type Theorems in Graded Integral Domains
It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky’s theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain, Bézout domain, valuation domain, Krull domain, π-domain).
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PROOF. Let A be a C*-algebra, ' a derivation of A. It is enough to show that the derivation is continuous on the self-adjoint portion As of A. Therefore if it is not continuous, by the closed graph theorem there is a sequence \xn\ (xn 4= 0) in As such that xn -»0 and xn -> a + ίέ(φθ), where a and b are self-adjoint. First, suppose that a =f= 0 and there exists a positive number λ(> 0) in the sp...
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ژورنال
عنوان ژورنال: Kyungpook mathematical journal
سال: 2011
ISSN: 1225-6951
DOI: 10.5666/kmj.2011.51.3.339