| 广义幂级数环的本质理想和非奇异性 |
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| 引用本文： | 肖民卿. 广义幂级数环的本质理想和非奇异性[J]. 数学杂志, 2010, 30(2) |
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| 作者姓名： | 肖民卿 |
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| 作者单位： | 福建师范大学数学与计算机科学学院,福建,福州,350007 |
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| 基金项目： | 福建省教育厅科研基金资助项日 |
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| 摘 要： | 本文研究了广义幂级数环与其系数环在本质理想和非奇异性上的关系.利用本质理想的定义和性质,得到了广义幂级数环的左理想为本质左理想的菪干充分必要条件.在此基础上,给出了广义幂级数环为左非奇异环的充分必要条件.
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| 关 键 词： | 严格偏序么半群 广义幂级数环 本质左理想 非奇异环 |
ESSENTIAL IDEALS AND NONSINGULARITY OF RINGS OF GENERALIZED POWER SERIES |
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| XIAO Min-qing. ESSENTIAL IDEALS AND NONSINGULARITY OF RINGS OF GENERALIZED POWER SERIES[J]. Journal of Mathematics, 2010, 30(2) |
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| Authors: | XIAO Min-qing |
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| Affiliation: | XIAO Min-qing(School of Math., Computer Science,Fujian Normal University,Fuzhou 350007,China) |
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| Abstract: | In this article,we study the relations between generalized power series rings and their coefficient rings on essential ideal and nonsingularity.By using the definition and properties of essential ideal of rings,we show some necessary and sufficient conditions for a left ideal to be a left essential ideal,and provide several necessary and sufficient conditions for generalized power series rings to be a left nonsingular ring. |
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| Keywords: | strictly ordered monoid ring of generalized power series essential ideal nonsingular ring |
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