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In this article we investigate the structure of rings in which lower nilradicals coincide with upper nilradicals. Such rings shall be said to be quasi-2-primal. It is shown first that the K$\ddot{\text{o}}$the's conjecture holds for quasi-2-primal rings. So the results in this article may provide interesting and useful information to the study of nilradicals in various situations. In the procedure we study the structure of quasi-2-primal rings, and observe various kinds of quasi-2-primal rings which do roles in ring theory.
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참고문헌 (21)
참고문헌 신청
D.D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26:2265~2272
R. Antoine / 2008 / Nilpotent elements and Armendariz rings / J. Algebra 319:3128~3140
E.P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Austral. Math. Soc 18:470~473
G.F. Birkenmeier / 1993 / Completely prime ideals and associated radicals / Proc. Biennial Ohio State-Denison Conference 1992 :102~129
G.F. Birkenmeier / 1997 / Regularity conditions and the sim-plicity of prime factor rings / J. Pure Appl. Algebra 115:213~230
R. Antoine / 2008 / Nilpotent elements and Armendariz rings / J. Algebra 319:3128~3140
E.P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Austral. Math. Soc 18:470~473
G.F. Birkenmeier / 1993 / Completely prime ideals and associated radicals / Proc. Biennial Ohio State-Denison Conference 1992 :102~129
G.F. Birkenmeier / 1997 / Regularity conditions and the sim-plicity of prime factor rings / J. Pure Appl. Algebra 115:213~230
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