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This article concerns a ring property which preserves the reversibility of elements at nonzero idempotents. A ring $R$ shall be said to be {\it quasi-reversible} if $0\neq ab\in I(R)$ for $a, b\in R$ implies $ba\in I(R)$, where $I(R)$ is the set of all idempotents in $R$. We investigate the quasi-reversibility of $2$ by $2$ full and upper triangular matrix rings over various kinds of reversible rings, concluding that the quasi-reversibility is a proper generalization of the reversibility. It is shown that the quasi-reversibility does not pass to polynomial rings. The structure of Abelian rings is also observed in relation with reversibility and quasi-reversibility.
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참고문헌 (16)
참고문헌 신청
D.D. Anderson / 1999 / Semigroups and rings whose zero products commute / Communications in Algebra 27(6):2847~2852
Ayman Badawi / 2007 / On abelian π-regular rings / Communications in Algebra 25(4):1009~1021
Howard E. Bell / 1970 / Near-rings in which each element is a power of itself / Bulletin of the Australian Mathematical Society 2(3):363~368
P. M. Cohn / 1999 / Reversible Rings / Bulletin of the London Mathematical Society 31(6):641~648
K. R. Goodearl / 1979 / von Neumann Regular Rings / Pitman (Advanced Publishing Program)
Ayman Badawi / 2007 / On abelian π-regular rings / Communications in Algebra 25(4):1009~1021
Howard E. Bell / 1970 / Near-rings in which each element is a power of itself / Bulletin of the Australian Mathematical Society 2(3):363~368
P. M. Cohn / 1999 / Reversible Rings / Bulletin of the London Mathematical Society 31(6):641~648
K. R. Goodearl / 1979 / von Neumann Regular Rings / Pitman (Advanced Publishing Program)
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