On prime right alternative rings with commutators in the left nucleus
1994 ◽
Vol 50
(2)
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pp. 287-298
Keyword(s):
A ring is called s–prime if the 2-sided annihilator of a nonzero ideal must be zero. In particular, any simple ring or prime (—1, 1) ring is s–prime. Also, a nonzero s–prime right alternative ring, with characteristic ≠ 2, cannot be right nilpotent. Let R be a right alternative ring with commutators in the left nucleus. Then R is associative in the following cases: (1) R is prime, with characteristic ≠ 2, and has an idempotent e ≠ 1 such that (e, e, R) = 0. (2) R is an algebra over a commutative-associative ring with 1/6, and R is either s–prime, or R is prime and locally (—1,1).
Keyword(s):
1997 ◽
Vol 25
(10)
◽
pp. 3147-3153
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2015 ◽
Vol 3
(1)
◽
pp. 1-12
Keyword(s):
1980 ◽
Vol 23
(3)
◽
pp. 299-303
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Keyword(s):
1991 ◽
Vol 44
(3)
◽
pp. 353-355
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1978 ◽
Vol 25
(3)
◽
pp. 322-327
Keyword(s):
1992 ◽
Vol 46
(1)
◽
pp. 81-90
2018 ◽
Vol 7
(1-2)
◽
pp. 19-26
Keyword(s):
2014 ◽
Vol 2
(2)
◽
pp. 18