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(英文)

Note of Intrinsic Submodules in Local Symmetric Bifurcation Problems With One State Variable

本文证明了Itr((?),Z2)=(Itr(?)(?){x}当且仅当Itr(?)由(?)中所有单项式生成,这里(?)是ε_(u,λ)中的理想且(?)=(?)(?){x}在(?)_(x,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.

In this paper, it is proved that Itr((?),Z2) = (Itr(?)). {x} if and only if Itr(?) is generated by all the monomials in (?), where (?) is an ideal of ε_(u,λ)and (?) = (?).{x} has finite Z2codirnension in (?)_(x,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.