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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
