关于强幂级数McCoy环

王文康

关于强幂级数McCoy环

王文康

1.
西北民族大学~~数学与计算机科学学院, 兰州 730124

详细信息

中图分类号: O153.3
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出版历程
- 收稿日期: 2013-05-01
- 修回日期: 2013-08-01
- 刊出日期: 2014-05-25

On strongly power-serieswise McCoy rings

WANG Wen-kang

1.
School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, China

摘要

摘要: 强幂级数McCoy环是幂级数McCoy环和强McCoy环的一个推广. 如果R是一个环， I是R的一个reduced理想，给出了如果R/I是强幂级数McCoy环(幂级数 McCoy环)，那么R是强幂级数McCoy环(幂级数McCoy环). 环R是幂级数McCoy环当且仅当R[x]是幂级数McCoy环. 找到了强幂级数McCoy环上的上三角矩阵环的一类强幂级数McCoy子环, 得出了幂级数McCoy环和reduced环是强幂级数McCoy环.
- McCoy环 /
- 强McCoy环 /
- 幂级数McCoy环 /
- 强幂级数McCoy环 /
- 上三角矩阵环
Abstract: In this paper, we introduce strongly power-serieswise McCoy rings, which are a generalization of power-serieswise McCoy rings and strongly McCoy rings, and investigate their properties. Let R be a ring and I an ideal of R such that I is reduced, we show that if R/I is strongly power-serieswise McCoy(resp., power-serieswise McCoy), then R is strongly power-serieswise McCoy(resp., power-serieswise McCoy). A ring R is power-serieswise McCoy if and only if R[x] is power-serieswise McCoy. We find that a class of strongly power-serieswise McCoy rings of upper triangular matrix ring over strongly power-serieswise McCoy rings. Meanwhile, we show that power-serieswise Armendariz rings and reduced rings are strongly power-serieswise McCoy rings.
- McCoy ring /
- strongly McCoy ring /
- power-serieswise McCoy ring /
- strongly power-serieswise McCoy ring /
- upper triangular matrix ring

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参考文献(1)

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