Some Radical Properties of Jordan Matrix Rings
Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 189-196
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Let A be a ring (not necessarily associative) in which 2x = a has a unique solution for each a ∈ A. Then it is known that if A contains an identity element 1 and an involution j : x ↦x and if Ja is the canonical involution on An determined by where the a i a l−l, 1 ≦ i ≦ n are symmetric elements in the nucleus of A then H(An, Ja), the set of symmetric elements of An, for n ≧ 3 is a Jordan ring if and only if either A is associative or n = 3 and A is an alternative ring whose symmetric elements lie in its nucleus [2, p. 127].
Rich, Michael. Some Radical Properties of Jordan Matrix Rings. Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 189-196. doi: 10.4153/CJM-1979-020-1
@article{10_4153_CJM_1979_020_1,
author = {Rich, Michael},
title = {Some {Radical} {Properties} of {Jordan} {Matrix} {Rings}},
journal = {Canadian journal of mathematics},
pages = {189--196},
year = {1979},
volume = {31},
number = {1},
doi = {10.4153/CJM-1979-020-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-020-1/}
}
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