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A property of reduced rings is proved in relation with centers, and our argument in this article is spread out based on this. It is also proved that the Wedderburn radical coincides with the set of all nilpotents in symmetric-over-center rings, implying that the Jacobson radical, all nilradicals, and the set of all nilpotents are equal in polynomial rings over symmetric-over-center rings. It is shown that reduced rings are reversible-over-center, and that given reversible-over-center rings, various sorts of reversible-over-center rings can be constructed.The structure of radicals in reversible-over-center and symmetric-over-center rings is also investigated.
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참고문헌 (13)
참고문헌 신청
S. A. Amitsur / 1956 / Radicals of polynomial rings / Canad. J. Math 8:355~361
D. D. Anderson / 1999 / Semigroups and rings whose zero products commute / Comm. Algebra 27(6):2847~2852
P. M. Cohn / 1999 / Reversible rings / Bull. London Math. Soc 31(6):641~648
J. L. Dorroh / 1932 / Concerning adjunctions to algebras / Bull. Amer. Math. Soc 38(2):85~88
K. R. Goodearl / 1979 / von Neumann regular rings / Pitman (Advanced Publishing Program)
D. D. Anderson / 1999 / Semigroups and rings whose zero products commute / Comm. Algebra 27(6):2847~2852
P. M. Cohn / 1999 / Reversible rings / Bull. London Math. Soc 31(6):641~648
J. L. Dorroh / 1932 / Concerning adjunctions to algebras / Bull. Amer. Math. Soc 38(2):85~88
K. R. Goodearl / 1979 / von Neumann regular rings / Pitman (Advanced Publishing Program)
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