杨文泽.幂群与序关系(英文)[J].数学研究及应用,1997,17(4):513~518 |
幂群与序关系(英文) |
Power Groups and Order Relations |
投稿时间:1994-06-25 |
DOI:10.3770/j.issn:1000-341X.1997.04.007 |
中文关键词: |
英文关键词:ordered group semigroup power group monoidal group. |
基金项目: |
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中文摘要: |
设G为非monoidal群,E是它的正规子集,满足E2=E并且1G∈/E.利用E作为正锥,可以在G上定义一个偏序,并且G成为一个偏序群.这样就可以利用这个序关系同时研究群G以及G上的以E为单位元的幂群.当E是极大子半群时,得到G的一个结构定理;在G是格序群的条件下,G上的幂群Γ可以膨胀为一个拟商群. |
英文摘要: |
Let G be a non-monoidal group, E be a normal subsemigroup of G such that E2=E and 1G∈/ E. Then we can define a partial order in G by setting E as the positive cone, and G becomes a partially ordered group. Then we can study both the group G and power group Гon G with identity E by the order. The structure of G is clear if the order is maximal and the power group Г on G can be expanded to be of quasi-quotient type if G is lattice ordered. |
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