| 相对于幺半群的拟-McCoy环 |
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| 引用本文： | 杨世洲,宋雪梅.相对于幺半群的拟-McCoy环[J].山东大学学报(理学版),2010,45(8):47-52. |
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| 作者姓名： | 杨世洲 宋雪梅 |
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| 作者单位： | 1. 西北师范大学数学与信息科学学院,甘肃,兰州,730070
2. 兰州城市学院数学学院,甘肃,兰州,730070 |
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| 摘 要： | 引入了M-拟-McCoy环并研究了其性质。对u.p.幺半群M,证明了reversible环是M-拟-McCoy环。对于包含无限循环子幺半群的交换可消幺半群M及u.p.幺半群N,若R是交换的M-拟-McCoy环,则RN]是M-拟-Mc-Coy环及R是M×N-拟-McCoy环。对幺半群M,R是M-拟-McCoy环当且仅当上三角矩阵环Tn(R)是M-拟-Mc-Coy环及直积∏i∈IRi是M-拟-McCoy环当且仅当每个Ri(i∈I)是M-拟-McCoy环。
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| 关 键 词： | 幺半群 u.p.幺半群 M-拟-McCoy环 M-拟-Armendariz环 上三角矩阵环 直积 |
| 收稿时间： | 2009-12-22 |
Quasi-McCoy rings relative to a monoid |
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| YANG Shi-zhou,SONG Xue-mei.Quasi-McCoy rings relative to a monoid[J].Journal of Shandong University,2010,45(8):47-52. |
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| Authors: | YANG Shi-zhou SONG Xue-mei |
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| Institution: | 1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, Gansu, China;
2. School of Mathematics, Lanzhou City University, Lanzhou 730070, Gansu, China |
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| Abstract: | M-quasi-McCoy rings are introduced, and their properties are investigated. It is shown that, for any unique product monoid M, every reversible ring is M-quasi-McCoy. If M is a commutative and cancellative monoid containing an infinite cyclic submonoid, N is a u.p. monoid and R is a commutative M-quasi McCoy ring, then R［N］ is M-quasi-McCoy and R is M×N-quasi-McCoy. For a monoid M, R is M-quasi-McCoy ring if and only if upper triangular matrix ring Tn(R) is M-quasi-McCoy ring and direct product ∏i∈IRi is M-quasi-McCoy ring if and only if each ring Ri(i∈I) is M-quasi-McCoy ring. |
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| Keywords: | monoid unique product monoid M-quasi-McCoy ring M-quasi-Armendariz ring upper triangular matrix ring direct product |
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