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Structure of minimal noncommutative duo rings and minimal strongly bounded non-duo rings
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This article is published in Communications in Algebra.The article was published on 1992-01-01. It has received 28 citations till now. The article focuses on the topics: Noncommutative geometry & Bounded function.read more
Citations
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A taxonomy of 2-primal rings
TL;DR: In this paper, it was shown that the (PSI) condition on a ring is left-right asymmetric, i.e., every factor ring modulo the right annihilator of a principal right ideal is 2-primal.
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Reversible and symmetric rings
TL;DR: In this paper, the precise relationships among three ring-theoretic conditions: reversible, symmetric and symmetric, and the effects of adjunction of unity on these conditions are investigated.
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Basic examples and extensions of symmetric rings
TL;DR: Recently, this article showed that polynomial rings over symmetric rings need not be symmetric and that classical right quotient rings of right symmetric ring are not symmetric.
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The Armendariz property on ideals
TL;DR: In this article, it was shown that a local ring is Armendariz, symmetric, and strongly reversible (hence ideal-armendariz) when the cardinality of the Jacobson radical is 4.
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On rings whose right annihilators are bounded
TL;DR: In this article, the authors introduce a condition that is a generalisation of strongly bounded rings and insertion-of-factors-property (IFP) rings, calling a ring strongly right AB if every non-zero right annihilator is bounded.
References
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Finite associative rings
TL;DR: In this article, the conditions générales d'utilisation (http://www.compositio.org/conditions) of the 1969 agreement with the Foundation Compositio Mathematica are described.
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Properties of primary noncommutative rings
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Finite-dimensional right duo algebras are duo
TL;DR: In this paper, it was shown that a right artinian ring with unity element is a duo ring, provided that the algebra is finite-dimensional modulo its radical and the square of the radical is zero.