Some properties of the Levitzki radical in alternative rings
1982 ◽
Vol 32
(1)
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pp. 52-60
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AbstractTwo local nilpotent properties of an associative or alternative ringAcontaining an idempotent are shown. First, ifA=A11+A10+A01+A00is the Peirce decomposition ofArelative toethen ifais associative or semiprime alternative and 3-torsion free then any locally nilpotent idealBofAiigenerates a locally nilpotent ideal 〈B〉 ofA. As a consequenceL(Aii) =Aii∩L(A)for the Levitzki radicalL. Also bounds are given for the index of nilpotency of any finitely generated subring of 〈B〉. Second, ifA(x)denotes a homotope ofAthenL(A)⊆L(A(x))and, in particular, ifA(x)is an isotope ofAthenL(A)=L(A(x)).
2015 ◽
Vol 3
(1)
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pp. 1-12
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1997 ◽
Vol 25
(10)
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pp. 3147-3153
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1992 ◽
Vol 35
(3)
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pp. 390-399
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1995 ◽
Vol 117
(3)
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pp. 431-438
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1966 ◽
Vol 9
(2)
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pp. 197-200
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2000 ◽
Vol 68
(1)
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pp. 126-130
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2019 ◽
Vol 19
(05)
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pp. 2050095
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