ARMENDARIZ PROPERTIES RELATIVE TO A RING ENDOMORPHISM

作者：Zhao Liang^*; Yan Xiaoguang

来源：Communications in Algebra, 2013, 41(9): 3465-3475.

DOI：10.1080/00927872.2012.688907

• Armendariz rings
• -Armendariz rings
• McCoy rings
• Weak -Armendariz rings
• 13B02
• 16W20
• 16S50

For an endomorphism of a ring R, we introduce the notion of an -Armendariz ring to investigate the relative Armendariz properties. This concept extends the class of Armendariz rings and gives us an opportunity to study Armendariz rings in a general setting. It is obvious that every Armendariz ring is an -Armendariz ring, but we shall give an example to show that there exists a right -Armendariz ring which is not Armendariz. A number of properties of this version are established. It is shown that if I is a reduced ideal of a ring R such that R/I is a right -Armendariz ring, then R is right -Armendariz. For an endomorphism of a ring R, we show that R is right -Armendariz if and only if R[x] is right -Armendariz. Moreover, a weak form of -Armendariz rings is considered in the last section. We show that in general weak -Armendariz rings need not be -Armendariz.

• 出版日期2013-9-2
• 单位南京晓庄学院; 安徽工业大学