The intersection of the powers of the radical in Noetherian P.I. rings |
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| Authors: | I N Herstein Lance W Small |
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| Institution: | (1) University of Chicago, Chicago, Illinois, U.S.A.;(2) Weizmann Institute, Rehovot, Israel;(3) University of California, San Diego, California |
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| Abstract: | LetR be a ring and J its radical. DefineJ
1=∩Jn, J2=∩J
1
n
,…,… Jk=∩J
k−1
n
.... It is shown that in a ringR satisfying a polynomial identity and the ascending chain condition on ideals,J
k
=0 for some appropriatek.
The work of the first author was supported by an NSF grant at the University of Chicago. The work of the second author was
supported by an NSF grant at the University of California, San Diego. |
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| Keywords: | |
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