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This article concerns the structure of idempotents in reversi\-ble and pseudo-reversible rings in relation with various sorts of ring extensions. It is known that a ring $R$ is reversible if and only if $ab\in I(R)$ for $a, b\in R$ implies $ab=ba$; and a ring $R$ shall be said to be {\it pseudo-reversible} if $0\neq ab\in I(R)$ for $a, b\in R$ implies $ab=ba$, where $I(R)$ is the set of all idempotents in $R$. Pseudo-reversible is seated between reversible and quasi-reversible. It is proved that the reversibility, pseudo-reversibility, and quasi-reversibility are equivalent in Dorroh extensions and direct products. Dorroh extensions are also used to construct several sorts of rings which are necessary in the process.
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참고문헌 (14)
참고문헌 신청
D.D. Anderson / 1999 / Semigroups and rings whose zero products commute / Communications in Algebra 27(6):2847~2852
P. M. Cohn / 1999 / Reversible Rings / Bulletin of the London Mathematical Society 31(6):641~648
J. L. Dorroh / 1932 / Concerning adjunctions to algebras / Bulletin of the American Mathematical Society 38(2):85~89
K. R. Goodearl / 1979 / von Neumann Regular Rings / Pitman (Advanced Publishing Program)
Harpreet K. Grover / 2009 / Rings with Multiplicative Sets of Primitive Idempotents / Communications in Algebra 37(8):2583~2590
P. M. Cohn / 1999 / Reversible Rings / Bulletin of the London Mathematical Society 31(6):641~648
J. L. Dorroh / 1932 / Concerning adjunctions to algebras / Bulletin of the American Mathematical Society 38(2):85~89
K. R. Goodearl / 1979 / von Neumann Regular Rings / Pitman (Advanced Publishing Program)
Harpreet K. Grover / 2009 / Rings with Multiplicative Sets of Primitive Idempotents / Communications in Algebra 37(8):2583~2590
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