Bulletin of the Korean Mathematical Society (대한수학회보)

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KAPLANSKY-TYPE THEOREMS IN GRADED INTEGRAL DOMAINS

  • CHANG, GYU WHAN (DEPARTMENT OF MATHEMATICS EDUCATION INCHEON NATIONAL UNIVERSITY) ;
  • KIM, HWANKOO (SCHOOL OF COMPUTER AND INFORMATION ENGINEERING HOSEO UNIVERSITY) ;
  • OH, DONG YEOL (DEPARTMENT OF MATHEMATICS EDUCATION CHOSUN UNIVERSITY)
  • Received : 2014.08.29
  • Published : 2015.07.31
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Abstract

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, $B{\acute{e}}zout$ domain, valuation domain, Krull domain, ${\pi}$-domain).

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References

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