대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제31권2호
  • /
  • Pages.237-246
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  • 2016
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON 𝜙-SHARP RINGS

  • Darani, Ahmad Yousefian (Department of Mathematics and Applications University of Mohaghegh Ardabili) ;
  • Rahmatinia, Mahdi (Department of Mathematics and Applications University of Mohaghegh Ardabili)
  • 투고 : 2015.05.01
  • 발행 : 2016.04.30
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초록

The purpose of this paper is to introduce some new class of rings that are closely related to the classes of sharp domains, pseudo-Dededkind domains, TV domains and finite character domains. A ring R is called a ${\phi}$-sharp ring if whenever for nonnil ideals I, A, B of R with $I{\supseteq}AB$, then I = A'B' for nonnil ideals A', B' of R where $A^{\prime}{\supseteq}A$ and $B^{\prime}{\supseteq}B$. We proof that a ${\phi}$-Dedekind ring is a ${\phi}$-sharp ring and we get some properties that by them a ${\phi}$-sharp ring is a ${\phi}$-Dedekind ring.

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참고문헌

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