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commutative groupoid的中文,翻译,解释,例句

commutative groupoid

commutative groupoid的基本解释
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The number of polynomial function over a finite commutative ring. This paper is on the basis of the research for the first question.With the structure of finite commutative ring,we know that a finite commutative ring can be expressed by direct sum of some finite commutative local rings.

本文主要基于对问题一的研究,并由有限交换环的构造可以知道,有限交换环可以由一些有限交换局部环的直和表示,于是就将问题简化到对有限交换局部环上多项式的判定。

Besides having a some insight into theinternal structure of operator algebras,it gives a greatimpetus to the development of modern mathematics towords thenon-commutative direction,especially to the developement ofnon-commutative geometry,non-commutative algebraical topologyas well as non-commutative algebraical geometry.

除了反映算子代数自身的内在性质之外,它还对于现代数学朝着非交换的方向发展起着积极的推动作用,特别对于&非交换微分几何&,&非交换的代数拓朴&,甚至&非交换的代数几何&等非交换的数学学科的发展具有重要的影响。

If R satisfies =0 for any elements x ,y in R then ⑴when k =1, R is commutative;⑵when R has the unity, R is commutative;⑶when R has at least one right regular element and f 2 (t 1,t2) has no terms with degree1 such that Fn= F then R iscommutative when R has at least one right regular element. Here we would like to point out that the above results generalized the results of Fu changlin ,moreover generalized some results of other references . This results enriched the commutative conditions of any ring.

若任取R 中元x, y均有=0 那么⑴k =1时R 为交换环;⑵R 有单位元时R 为交换环;⑶f_2 (t_1,t_2)中t_2的次数不小于k -1且R 中至少有一个右正则元时R 为交换环。

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