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This article is cited in 2 scientific papers (total in 2 papers)
A note on locally nilpotent rings with chain conditions
K. A. Zhevlakov Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR
Abstract:
It is shown that a locally nilpotent ring with maximality condition for two-sided ideals is nilpotent. The restriction on the characteristic in one of the author's previously published theorems is lifted. A one-sided nil-ideal of an alternative ring, satisfying the maximality condition for right ideals, is a nilpotent ring. An example is constructed of a commutative locally nilpotent ring $A$ with maximality condition for ideals which is idempotent: $A=A^2$.
Received: 30.03.1972
Citation:
K. A. Zhevlakov, “A note on locally nilpotent rings with chain conditions”, Mat. Zametki, 12:2 (1972), 121–126; Math. Notes, 12:2 (1972), 507–509
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https://www.mathnet.ru/eng/mzm9857 https://www.mathnet.ru/eng/mzm/v12/i2/p121
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Abstract page: | 160 | Full-text PDF : | 83 | First page: | 1 |
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