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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 $A'\supseteq A$ and $B'\supseteq B$. 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 (16)
참고문헌 신청
Z. Ahmad / 2012 / A Schreier domain type condition / Bull.Math. Soc. Sci. Math. Roumania 55(3):241~247
D. F. Anderson / 2004 / On Φ-Prufer rings and Φ-Bezout rings / Houston J. Math 30(2):331~343
A. Badawi / 1999 / On Φ-pseudo-valuation rings / Lecture Notes Pure Appl. Math. 205:101~110
A. Badawi / 1999 / On divided commutative rings / Comm. Algebra 27(3):1465~1474
A. Badawi / 2000 / On Φ-pseudo-valuation rings. II / Houston J. Math 26(3):473~480
D. F. Anderson / 2004 / On Φ-Prufer rings and Φ-Bezout rings / Houston J. Math 30(2):331~343
A. Badawi / 1999 / On Φ-pseudo-valuation rings / Lecture Notes Pure Appl. Math. 205:101~110
A. Badawi / 1999 / On divided commutative rings / Comm. Algebra 27(3):1465~1474
A. Badawi / 2000 / On Φ-pseudo-valuation rings. II / Houston J. Math 26(3):473~480
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