The ideals in (-1,1) rings
2014 ◽
Vol 3
(1)
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pp. 22
A (-1, 1) ring \(R\) contains a maximal ideal \(I_{3}\) in the nucleus \(N\). The set of elements \(n\) in the nucleus which annihilates the associators in (-1, 1) ring \(R\), \(n(x, y, z) = 0\) and \((x, y, z)n = 0\) for all \(x, y, z \in R\) form the ideal \(I_{3}\) of \(R\). Let \(I\) be a right ideal of a 2-torsion free (-1, 1) ring \(R\) with commutators in the middle nucleus. If \(I\) is maximal and nil, then \(I\) is a two sided ideal. Also if \(I\) is minimal then it is either a two-sided ideal, or the ideal it generates is contained in the middle nucleus of \(R\) and the radical of \(R\) is contained in \(P\) for any primitive ideal \(p\) of \(R\).
1999 ◽
Vol 51
(1)
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pp. 147-163
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1961 ◽
Vol 57
(1)
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pp. 1-7
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1955 ◽
Vol 7
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pp. 169-187
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2019 ◽
Vol 62
(3)
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pp. 847-859
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1996 ◽
Vol 54
(1)
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pp. 41-54
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1966 ◽
Vol 18
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pp. 1183-1195
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