| 幺半群环上的McCoy定理 |
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| 引用本文： | 宿维军.幺半群环上的McCoy定理[J].高师理科学刊,2009,29(4):28-29. |
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| 作者姓名： | 宿维军 |
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| 作者单位： | 西北师范大学数学与信息科学学院,甘肃,兰州,730070;甘肃民族师范学院数学系,甘肃合作747000 |
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| 摘 要： | McCoy在文献1]中证明了定理:如果R是交换环,若g(x)是Rx]中的零因子,则存在一个非零元c∈R,使得cg(x)=0.对于这个结论Hirano在文献2]中将其推广到非交换环上,Cortes在文献3]中推广到自同构形式的斜多项式环上.将此结论推广到幺半群环上,即有:设R为环,M为唯一积幺半群或(M,<)是严格全序幺半群,α∈RM].若rAnn RM](αRM])≠0,则rAnn RM](αRM])∩R≠0.
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| 关 键 词： | 幺半群环 零化子 McCoy定理 |
On McCoy theorem over monoid rings |
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| SU Wei-jun.On McCoy theorem over monoid rings[J].Journal of Science of Teachers＇College and University,2009,29(4):28-29. |
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| Authors: | SU Wei-jun |
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| Institution: | 1.School of Mathematics and Information Science;Northwest Normal University;Lanzhou 730070;China;2.Department of Mathematics;Gansu Normal College for Minorities;Hezuo 747000;China |
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| Abstract: | In the reference 1],McCoy proved the following theorem:If R be a commutative ring,g(x)be a zero divisor in R x],then exist a nonzero element c∈ R,such that cg(x)=0.Hirano generalized this conclusion to noncommutative ring in the reference 2],the reference 3] had generalized this conclusion to skew polynomial ring of automorphism type.Generalized McCoy theorem to monoid rings:If R be a ring,M a unique product monoid or(M,<)be a totally ordered monoid α ∈RM].If rAnn R M](α RM])≠0,then rAnn R M](αR M])∩R≠0. |
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| Keywords: | monoid ring annihilator McCoy theorem |
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