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This article mainly concentrates on the open question wheth\-er a right self-injective ring $R$ is necessary QF if $R/S_l$ is left Goldie. It is answered affirmatively under the condition $S_l\subseteq S_r$, where $S_l$ and $S_r$ denote the left socle and right socle of $R$ respectively. And the original condition ``right self-injective" can be weakened to ``right CS and right P-injective". It is also proved that a semiperfect, left and right mininjective ring $R$ is QF if $S_r\subseteq^{ess}R_R$ and $R/S_l$ is left Goldie.
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참고문헌 (14)
참고문헌 신청
P. Ara / 1991 / On continuous semiprimary rings / Comm. Algebra 19(7):1945~1957
E. P. Armendariz / 1980 / Rings with DCC on essential left ideals / Comm. Algebra 8(3):299~308
E. P. Armendariz / 1992 / Self-injective rings with restricted chain conditions / Arch. Math. (Basel) 58(1):24~33
J. Chen / 2014 / Ring theory and its applications / Amer. Math. Soc. :45~68
J. Chen / 2007 / Characterizations of QF rings / Comm. Algebra 35(1):281~288
E. P. Armendariz / 1980 / Rings with DCC on essential left ideals / Comm. Algebra 8(3):299~308
E. P. Armendariz / 1992 / Self-injective rings with restricted chain conditions / Arch. Math. (Basel) 58(1):24~33
J. Chen / 2014 / Ring theory and its applications / Amer. Math. Soc. :45~68
J. Chen / 2007 / Characterizations of QF rings / Comm. Algebra 35(1):281~288
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