| 摘要: |
| R中的理想I是可消理想的定义，提出在（冯诺依曼）正则算术环中建立可消理想的一个等价刻画；通过映射φ:Lat(R)→Lat(I)：对于任意的A∈Lat(R),φ(A)=I∩A，寻找环R和理想I的进一步关系，得出对于任意的0≠e∈Idem(R)，存在0≠f∈Idem(I)使得Re=Rf;从而给出完全算术环中可消理想的等价条件：R是一个完全算术环且J(R)=0，那么I是一个可消理想当且仅当对于任意e∈Idem(R)，存在f∈Idem(I)使得Re=Rf. |
| 关键词: 正则环 可消理想 完全不可约理想 完全算术环 |
| DOI： |
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| A Characterization for Cancellation Ideals |
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XU Jing wen
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| Abstract: |
| As for the definition of an ideal I of a commutative ring R which is called a cancellation ideal, this paper establishes an equivalent characterization for cancellation ideals in a (von Neumann) regular arithmetical ring, uses the map φ:Lat(R)→Lat(I):for any A∈Lat(R),φ(A)=I∩A to study the relationship between R and I, then successfully gets the conclusion that 0≠e∈Idem(R), there exists 0≠f∈Idem(I), such that Re=Rf, therefore gives the equivalent condition for cancellation ideal in completely arithmetical ring: R is a completely arithmetical ring and J(R)=0, then I is a cancellation ideal if and only if for any e∈Idem(R), there exists f∈Idem(I), so that Re=Rf. |
| Key words: regular ring cancellation ideal completely irreducible ideal completely arithmetical ring |
