1) Graded trivial extension
分次平凡扩张
2) trivial extension
平凡扩张
1.
After defining the k-functor F over X, proves that the trivial extension categoty X∝F is also G-graded.
在定义C上k-函子F的基础上,证明了平凡扩张范畴C∝F仍为k上G-分次范畴;当F为X上分次k-函子时,给出了一族范畴同构,即r∈N(G),有(C#G)∝(F#r)(C∝F)r#G。
2.
We investigate the semicommutative properties of those rings under the reduced condition which are more generalized than trivial extensions.
讨论了在约化条件下,比平凡扩张更广泛的一类扩张环的半交换性。
3.
Given a c commutative ring R , obtains some conditions such that the skew power series ring R[[x,α]] and the trivial extension R∝M are also c commutative,and give examples to show these conditions are necessary.
对于 c-可换环 R,给出条件使得斜幂级数环 R[[x,α]]和 R的平凡扩张 R∝Μ也为 c-可换环 ,并用例子说明这些条件是必要的 。
4) trivial graded extension
分次扩张
1.
Secondly,a one-to-one correspondence between the set of all trivial graded extensions of V in K[Z(2),σ] and the set of all pure cones in Z(2) is proved.
首先,给出Z(2)上纯锥的完全刻画;然后,证明了Z(2)上的纯锥的集合和K[Z(2),σ]上的平凡分次扩张的集合之间有一个一一对应的关系;最后,对K[Z(2),σ]上的平凡分次扩张进行完全的刻画。
5) graded excellent extension
分次Excellent扩张
1.
The concept of graded excellent extension of graded rings is introduced.
本文引进了分次环的分次Excellent扩张概念,设S=⊕_(g∈G)S_g是R=⊕_(g∈G)R_g的分次Excellent扩张,证明了S是分次右V-环当且仅当R是分次右V-环,S是分次PS-环当且仅当R是分次PS-环,S是分次Von Neumann正则环当且仅当R是分次Von Neumann正则环。
6) Weakly graded radical extension
弱分次根扩张环
补充资料：极大扩张和极小扩张
极大扩张和极小扩张
maximal and minimal extensions
极大扩张和极小扩张匡.习的司出目.公油抽lex妇心.旧;MaKcl.Ma刀‘.oe H Mll.”M田.妇oe PaC山一Pe皿朋] 一个对称算子(s笋nr贺苗c opemtor)A的极大扩张和极小扩张分别是算子牙(A的闭包，(见闭算子(cfo“月。详mtor”)和A’(A的伴随，见伴随算子(呐。int opera.tor)).A的所有闭对称扩张都出现在它们之间.极大扩张和极小扩张相等等价于A的自伴性(见自伴算子(义休.adjoint operator))，并且是自伴扩张唯一性的必要和充分条件.A.H.J’Ior朋oB，B.c.lll户、MaR撰
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参考词条