NIL-ARMENDARIZ RINGS AND UPPER NILRADICALS

作者：Jung Da Woon^*; Kim Nam Kyun; Lee Yang; Yang Sung Pil

来源：International Journal of Algebra and Computation, 2012, 22(6): 1250059.

DOI：10.1142/S0218196712500592

• Nil-Armendariz ring
• Armendariz ring
• polynomial ring
• nilpotent element
• nilradical
• von Neumann regular ring

We continue the study of nil-Armendariz rings, initiated by Antoine, and Armendariz rings. We first examine a kind of ring coproduct constructed by Antoine for which the Armendariz, nil-Armendariz, and weak Armendariz properties are equivalent. Such a ring has an important role in the study of Armendariz ring property and near-related ring properties. We next prove an Antoine%26apos;s result in relation with the ring coproduct by means of a simpler direct method. In the proof we can observe the concrete shapes of coefficients of zero-dividing polynomials. We next observe the structure of nil-Armendariz rings via the upper nilradicals. It is also shown that a ring R is Armendariz if and only if R is nil-Armendariz if and only if R is weak Armendariz, when R is a von Neumann regular ring.

• 出版日期2012-9