| 单状态变量的局部对称性分岔问题中内蕴子模的一点注记 |
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| 引用本文： | 时红廷,郑崇友. 单状态变量的局部对称性分岔问题中内蕴子模的一点注记[J]. 数学进展, 2005, 34(3): 309-312 |
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| 作者姓名： | 时红廷 郑崇友 |
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| 作者单位： | 首都师范大学数学系,北京,100037 |
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| 基金项目： | Supported by the NSFC(No．10371079 and No．10471099)． |
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| 摘 要： | 本文证明了Itr(^→T，Z2)=(ItrT)．{x}当且仅当ItrT由T中所有单项式生成，这里T是εu，λ中的理想且T=T．{x}在^→εx，λ(Z2)中具有有限Z2余维数，此结果表明，Golubitsky的书中关于最大内蕴理想和最大内蕴子模的关系式是错误的，本文最后给出了反例。
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| 关 键 词： | 分岔 理想 内蕴理想 子模 内蕴子模 |
Note of Intrinsic Submodules in Local Symmetric Bifurcation Problems With One State Variable |
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| SHI Hong-ting,ZHENG Chong-you. Note of Intrinsic Submodules in Local Symmetric Bifurcation Problems With One State Variable[J]. Advances in Mathematics(China), 2005, 34(3): 309-312 |
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| Authors: | SHI Hong-ting ZHENG Chong-you |
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| Abstract: | In this paper, it is proved that Itr(→T,Z2) = (ItrT). {x} if and only if ItrT is generated by all the monomials in T, where T is an ideal of εu,λ and →T = T. {x} has finite Z2codimension in →εx,λ(Z2). This result show that the relationship between the largest intrinsic ideal and the largest intrinsic submodule given in the book of Golubitsky is wrong. A counter example is given at last. |
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| Keywords: | bifurcation ideal intrinsic ideal submodule intrinsic submodule |
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