1) locally finite sum
局部有限和
2) locally finite
局部有限
1.
The notion of base-countably paracompact space is introduced and some of its equivalent characterizations are obtained:(i)X is a base-countably paracompact space if there exsists an open basis B for X with |B|=ω(X) such that every countably open cover U={Ui}i∈N of X has a locally finite countabe refinement B′ by members of B,B′={Bi}i∈N and BiUi.
引入了基-可数仿紧空间的概念,给出基-可数仿紧空间的一些等价刻画,获得以下结果:(i)X是基-可数仿紧空间当且仅当存在X的一开基B,|B|=ω(X),对于X的每一可数开覆盖U={Ui}i∈N,都存在B′B,使得B′={Bi}i∈N是U的局部有限的可数开加细,且BiUi;(ii)设X是正规空间,X是基-可数仿紧空间当且仅当存在的一开基B,|B|=ω(X),使得X的每一可数开覆盖都存在由B中的元构成的局部有限的收缩。
2.
Author mainly proves following:(1)X is a Base-paracompact space iff X is a Base-countably paracompact space and every open cover of X has a σ-locally finite open refinement by members of the basis which witnesses Base-countably paracompact space.
主要证明了如下结果:(1)X是基-仿紧空间当且仅当X是基-可数仿紧空间,并且X的每一开覆盖都存在满足X是基-可数仿紧空间的开基的元构成的σ-局部有限的开加细。
3.
In [4], the authors have proved that if a locally finite group is a core-finite, then it .
文[4]证明了局部有限的Core-有限群是abelian-by-finite。
3) finite local
有限局部环
1.
Let R=Z/pk Z is a finite local ring of module integer pk,Let D i=O Di - Di O ,Δ ={Pi∈ GL2 si ( R) | Pi D i Pi′- D i=B},and matrix B=pμBis a arbitrary alternate matrix with order2 siover R,where p is a prime and k>1 ,Di=diag{pri,… ,pri},0 <ri<k,ri<μ≤ k,si≥ 1 .
设 R=Z/pk Z是模整数 pk的有限局部环 ,Di=O Di-Di O ,B=pμB是 R上任意取定的 2 si阶交错阵 ,Δ={Pi∈ GL2 si( R) |Pi Di Pi′-Di=B},其中 Di=diag{pri,… ,pri},0
4) locally finite group
局部有限群
1.
The following results have been given: let R be a ring and G be a locally finite group,if the group ring RG is a left G-morphic ring,then R is a left G-morphic ring;if the group ring RH is a left G-morphic ring for every finite subgroup H of G,then the group ring RG is a left G-morphic ring.
本文讨论了左G-morphic群环RG的性质,主要证明了以下结果:设R是一个环,G是一个局部有限群,如果群环RG是左G-morphic环,那么R是左G-morphic环;如果对G的每个有限子群H,群环RH是左G-morphic环,那么群环RG是左G-morphic环。
2.
For every subgroup H of a locally finite group G, if H is a weakly semi-radicable group and H ≠ Hp for every p∈ π(H), then G is a locally nilpotent group and every Sylow p-subgroup of G is finite.
证明了:①如果局部有限群G的每一个子群H是弱半根群且对任意p∈π(H)满足H≠Hp,那么G是局部幂零群而且每一个Sylow p-子群是有限群。
5) finite local ring
有限局部环
1.
Taking the set of all 3×3 alternate matrices over finite local ring Z/pmZ as the set of treatments.
利用有限局部环Z/pmZ上的全体3×3矩阵作为处理的集合,构作了有m个结合类的结合方案,并且计算出其参数。
2.
Let H be a 3×3 alternate matrices over finite local ring Z/pmZ.
设H是有限局部环Z/pmZ上的3×3交错矩阵,通过确定H的标准形,计算出有限局部环Z/pmZ上合同标准形的3×3交错矩阵的个数nk,其中当0≤k
3.
Nan jizhu takes the set of all 2× 2 alternate matrices over finite local ring as the set of treatments and obtains an association scheme with m associate classes,whose parameters are also computed.
南基洙利用有限局部环上的2阶交错矩阵构作了多个结合类的结合方案,并计算了参数。
6) strong locally finite family
强局部有限
补充资料：局部有限群
局部有限群
locally finite group
局部有限群【】叨uy五‘teg心甲;.Ka月研。幼邢，翻rPynna] 每一有限生成子群皆有限的群.任意局部有限群是一个扭群(见周期群(详石浏c脚uP))，但反之未必成立(见R川亩山问题(Burnside prob七m)).一个局部有限群被另一局部有限群的扩张仍是局部有限群.满足子群(甚至是Abel子群)的极小条件的每个局部有限群均包含一个指数有限的Abel子群(【3」)(见具有有限性条件的群(gro叩俪tha血址n郎co画-tion)).一个其Abel子群具有有限秩(见群的秩(扭瓜of ag心tlP))的局部有限群本身亦具有有限秩，且包含一个有限指数的局部可解子群(见局部可解群(1.llysol姐ble grouP)).
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条