Supplementing Radicals and Decompositions of Near-Rings |
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Authors: | G. F. Birkenmeier R. Wiegandt |
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Affiliation: | (1) Department Of Mathematics, University Of Louisiana At Lafayette, Lafayette, La, 70504 1010, U.S.A. |
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Abstract: | If is a radical of near-rings and is its supplementing radical, then (N)(N) N. We address the issue when (N) (N) = N holds. In the variety F of near-rings in which the constants form an ideal, the assignment c: N Nc is a hereditary Kurosh–Amitsur radical, c is characterized in terms of distributors and criteria are given for the decomposition N = c(N) c(N). In the subvariety A of all abstract affine near-rings, assigning the maximal torsion ideal (N) is a hereditary Kurosh–Amitsur radical. If such near-rings N A satisfy dcc on principal right ideals, then N splits into a direct sum N = (N) (N) where the additive group of (N) is torsionfree and divisible. Dropping dcc on principal right ideals, an ``essential" decomposition result is proved. |
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Keywords: | radical and supplementing radical of near-rings torsion radical of abstract affine near-rings essential decomposition |
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