Extensions of Generalized Reduced Rings

• 来源期刊: 代数集刊（英文版）
• 关键词: reduced rings 2-primal rings Armendariz rings polynomial rings
• 年，卷（期）: 2005,（2）
• 页码范围: 229-240
• 页数: 12页
• 语种: 英文

摘要

Anderson and Camillo studied the class of rings satisfying ZCn for n ≥2, which is a generalization of reduced rings. In this paper, we continue the study of such rings. We observe several extensions of rings satisfying ZCn. Rings satisfying the zero insertion property for n (simply, ZIn), which is a generalization of ZCn, are also introduced. In particular, we prove that every ring satisfying ZIn for some n ≥ 2 is a 2-primal ring. Furthermore, if R is an Armendariz ring satisfying ZIn for n ≥ 2, then the polynomial ring R[x] over R also satisfies ZIn.