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 <TEX>${\phi}$</TEX>-sharp ring if whenever for nonnil ideals I, A, B of R with <TEX>$I{\supseteq}AB$</TEX>, then I = A'B' for nonnil ideals A', B' of R where <TEX>$A^{\prime}{\supseteq}A$</TEX> and <TEX>$B^{\prime}{\supseteq}B$</TEX>. We proof that a <TEX>${\phi}$</TEX>-Dedekind ring is a <TEX>${\phi}$</TEX>-sharp ring and we get some properties that by them a <TEX>${\phi}$</TEX>-sharp ring is a <TEX>${\phi}$</TEX>-Dedekind ring.

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