A CONCEPT UNIFYING THE ARMENDARIZ AND NI CONDITIONS

作者：Chun Young^*; Jeon Young Cheol; Kang Sungkyung; Lee Key Nyoung; Lee Yang

来源：Bulletin of the Korean Mathematical Society, 2011, 48(1): 115-127.

DOI：10.4134/BKMS.2011.48.1.115

• NR ring
• NI ring
• Armendariz ring
• matrix ring

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.

• 出版日期2011-1