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A CONCEPT UNIFYING THE ARMENDARIZ AND NI CONDITIONS
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 Title & Authors
A CONCEPT UNIFYING THE ARMENDARIZ AND NI CONDITIONS
Chun, Young; Jeon, Young-Cheol; Kang, Sung-Kyung; Lee, Key-Nyoung; Lee, Yang;
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 Abstract
We study the structure of the set of nilpotent elements in various kinds of ring and introduce the concept of NR ring as a generalization of Armendariz rings and NI rings. We determine the precise relationships between NR rings and related ring-theoretic conditions. The Kothe`s conjecture is true for the class of NR rings. We examined whether several kinds of extensions preserve the NR condition. The classical right quotient ring of an NR ring is also studied under some conditions on the subset of nilpotent elements.
 Keywords
NR ring;NI ring;Armendariz ring;matrix ring;
 Language
English
 Cited by
1.
On linearly weak Armendariz rings, Journal of Pure and Applied Algebra, 2015, 219, 4, 1122  crossref(new windwow)
2.
Polynomial Rings Over Weak Armendariz Rings need not be Weak Armendariz, Communications in Algebra, 2014, 42, 6, 2528  crossref(new windwow)
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