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http://dx.doi.org/10.4134/CKMS.2016.31.2.237

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)
Publication Information
Communications of the Korean Mathematical Society / v.31, no.2, 2016 , pp. 237-246 More about this Journal
Abstract
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.
Keywords
${\phi}$-sharp ring; ${\phi}$-pseudo-Dedekind ring; ${\phi}$-TV ring; ${\phi}$-finite character ring;
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