• Title/Summary/Keyword: ${\phi}$-pseudo-Dedekind ring

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ON 𝜙-SHARP RINGS

  • Darani, Ahmad Yousefian;Rahmatinia, Mahdi
    • Communications of the Korean Mathematical Society
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    • v.31 no.2
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    • pp.237-246
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    • 2016
  • 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.