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