A commutativity theorem for power-associative rings
1970 ◽
Vol 3
(1)
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pp. 75-79
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Let R be a power-associative ring with identity and let I be an ideal of R such that R/I is a finite field and x ≡ y (mod I) implies x2 = y2 or both x and y commute with all elements of I. It is proven that R must then be commutative. Examples are given to show that R need not be commutative if various parts of the hypothesis are dropped or if “x2 = y2” is replaced by “xk = yk” for any integer k > 2.
2016 ◽
Vol 26
(05)
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pp. 985-1017
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1990 ◽
Vol 13
(4)
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pp. 769-774
Keyword(s):
2019 ◽
Vol 18
(07)
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pp. 1950131
1985 ◽
Vol 32
(3)
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pp. 357-360
1953 ◽
Vol 49
(4)
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pp. 590-594
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1978 ◽
Vol 25
(3)
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pp. 322-327
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2013 ◽
Vol 89
(3)
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pp. 503-509
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2019 ◽
Vol 12
(2)
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pp. 622-648
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