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 A concept unifying the Armendariz and NI conditions Bull. Korean Math. Soc. 2011 Vol. 48, No. 1, 115-127 https://doi.org/10.4134/BKMS.2011.48.1.115Printed January 1, 2011 Young Chun, Young Cheol Jeon, Sungkyung Kang, Key Nyoung Lee, and Yang Lee Korea Science Academy, Korea Science Academy, Korea Science Academy, Korea Science Academy, Pusan National University 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 K\"othe'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 MSC numbers : 16D25, 16N40 Downloads: Full-text PDF