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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 787-801, October 2007




BROWN-McCOY RADICALS FOR NEAR-RINGS


BY


RAVI SRINIVASA RAO AND T. SUJATHA




Abstract. In this paper two more radicals B$ ^{s}_{1}$ and B $ ^{s}_{1(0)}$ are introduced for near-rings which generalize the Brown-McCoy radical of rings. It is proved that B$ ^{s}_{1}$ is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings but it is not a KA-radical in the class of all near-rings. Moreover, B $ ^{s}_{1(0)}$ is a KA-radical in the class of all near-rings and for a near-ring R, B $ ^{s}_{1(0)}$(I) $ \subseteq$ B $ ^{s}_{1(0)}$(R) $ \cap$ I for all ideals I of R and the equality holds if I is a left invariant ideal of R.

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Received September 5, 2006; revised February 20, 2007.

AMS Subject Classification. 16Y30.

Key words. Brown-McCoy radicals of near-rings, weakly G-regular elements of type-$ \nu$, weakly $ \nu$-semi-nilpotent elements.