数学进展
數學進展
수학진전
ADVANCES IN MATHEMATICS
2005年
3期
309-312
,共4页
分岔%理想%内蕴理想%子模%内蕴子模
分岔%理想%內蘊理想%子模%內蘊子模
분차%이상%내온이상%자모%내온자모
bifurcation%ideal%intrinsic ideal%submodule%intrinsic submodule
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.
本文證明瞭Itr(→T,Z2)=(ItrT).{x}噹且僅噹ItrT由T中所有單項式生成,這裏T是εu,λ中的理想且→T=T·{x}在→εx,λ(Z2)中具有有限Z2餘維數.此結果錶明,Golubitsky的書中關于最大內蘊理想和最大內蘊子模的關繫式是錯誤的,本文最後給齣瞭反例.
본문증명료Itr(→T,Z2)=(ItrT).{x}당차부당ItrT유T중소유단항식생성,저리T시εu,λ중적이상차→T=T·{x}재→εx,λ(Z2)중구유유한Z2여유수.차결과표명,Golubitsky적서중관우최대내온이상화최대내온자모적관계식시착오적,본문최후급출료반례.
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.
