대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제58권6호
  • /
  • Pages.1401-1407
  • /
  • 2021
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON GRADED RADICALLY PRINCIPAL IDEALS

  • 투고 : 2020.11.15
  • 심사 : 2021.02.18
  • 발행 : 2021.11.30
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초록

Let R be a commutative G-graded ring with a nonzero unity. In this article, we introduce the concept of graded radically principal ideals. A graded ideal I of R is said to be graded radically principal if Grad(I) = Grad(〈c〉) for some homogeneous c ∈ R, where Grad(I) is the graded radical of I. The graded ring R is said to be graded radically principal if every graded ideal of R is graded radically principal. We study graded radically principal rings. We prove an analogue of the Cohen theorem, in the graded case, precisely, a graded ring is graded radically principal if and only if every graded prime ideal is graded radically principal. Finally we study the graded radically principal property for the polynomial ring R[X].

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과제정보

The author would like to thank the referee for his/her great efforts in proofreading the manuscript.

참고문헌

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