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Let $R$ be a ring with identity and $J(R)$ denote the Jacobsonradical of $R$, i.e., the intersection of all maximal left ideals of $R$. A ring $R$ is called {\it $J$-symmetric} if for any $a,b,c\in R$, $abc = 0$ implies $bac \in J(R)$. We prove that some results of symmetric rings can be extended to the $J$-symmetric rings for this general setting. We give many characterizations of such rings. We show that the class of $J$-symmetric rings lies strictly between the class of symmetric rings and the class of directly finite rings.
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참고문헌 (13)
참고문헌 신청
V. P. Camillo / 1994 / Exchange rings, units and idempotents / Comm. Algebra 22(12):4737~4749
H. Chen / 2010 / On strongly J-clean rings / Comm. Algebra 38(10):3790~3804
J. L. Dorroh / 1932 / Concerning adjunctions to algebras / Bull. Amer. Math. Soc 38(2):85~88
C. Huh / 2005 / Basic examples and extensions of symmetric rings / J. Pure Appl. Algebra 202(1-3):154~167
P. A. Krylov / 2009 / Modules over formal matrix rings / Fundam. Prikl. Mat 15(8):145~211
H. Chen / 2010 / On strongly J-clean rings / Comm. Algebra 38(10):3790~3804
J. L. Dorroh / 1932 / Concerning adjunctions to algebras / Bull. Amer. Math. Soc 38(2):85~88
C. Huh / 2005 / Basic examples and extensions of symmetric rings / J. Pure Appl. Algebra 202(1-3):154~167
P. A. Krylov / 2009 / Modules over formal matrix rings / Fundam. Prikl. Mat 15(8):145~211
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