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 分式域
 “分式域”译为未确定词的双语例句
 The fraction of A is denoted by A' = Q(v). A'=Q(v)是A的分式域。 短句来源 A =Q(v) is the fraction field of A. A=Q(v)是A的分式域。 短句来源 Let v is an indeterminate, A=Z[v,v~-1], A =Q(v) is the fraction field of A. 令v是未定元,A=Z[v,v~(-1)],A′=Q(v)是A的分式域。 短句来源 R' is the fraction of R. U' is a quantum algebra over R' associated to Cartan matrix (a_(ij)) . U is a subquantum algebra over R of U' . R′是R的分式域，U′是R′上相伴于R′的Caftan矩阵的量子代数，U是R上的量子代数，它是U′的R子代数。 短句来源
 相似匹配句对
 A =Q(v) is the fraction field of A. A=Q(v)是A的分式域。 短句来源 The fraction of A is denoted by A' = Q(v). A'=Q(v)是A的分式域。 短句来源 John Domains John域 短句来源 DECONVOIVTWN OF THE FREQUENCY DOMAIN 频率域反褶积 短句来源 Interpolation by Continued Fractions 连分式插值 短句来源

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 field of fractions
 We show that the absolute invariants (i.e.,the ${\mbox{\rm GL}}(2, {\mbox{\bf R}})$-invariants in the field of fractions of ${\mathcal P}$) distinguish the isomorphism classes of 2-dimensional non-associative real division algebras. Let R be a regular local ring, K its field of fractions and A an Azumaya algebra with involution over R. We give necessary and sufficient conditions in terms of matrix cones for (i) an epic R-field to be orderable, (ii) a full order on R to be extendable to a field of fractions of R and (iii) for such an extension to be unique. Let A be a domain of field of fractions K, and A[X]sub the ring of "integral valued polynomials over A", i. Denote by K its field of fractions and by k its residue field. 更多
 fractional domain
 The first assumes a partial spatiotemporalization of consciousness into a fractional domain located between three and four dimensions.
 In this paper,we consider reduced groups of group rings.As applications,we obtainthe following results:(1)R is a commutative semihereditary ring with torsion reduced group if and only if there exists some s > 0 such that for any finitely generated semireflexiveR-module P.(2)Let R a semilocal Dedekind domain,G be a finitely generated abellan group.Then K_0RG is a torsion group if and only if whenever G has some element of primeorder p.(3)Suppose K_0RG is a torsion group. If L is the fractional field of integral... In this paper,we consider reduced groups of group rings.As applications,we obtainthe following results:(1)R is a commutative semihereditary ring with torsion reduced group if and only if there exists some s > 0 such that for any finitely generated semireflexiveR-module P.(2)Let R a semilocal Dedekind domain,G be a finitely generated abellan group.Then K_0RG is a torsion group if and only if whenever G has some element of primeorder p.(3)Suppose K_0RG is a torsion group. If L is the fractional field of integral domain Rand [G∶H]<∞,then for any . 本文系统地研究群环的约化群，利用约化群刻划了群环上模的结构。主要结果：（１）Ｒ为交换半遗传环且Ｋ＿０Ｒ为挠群ｉｆｆ对任何有限生成半自反Ｒ－模Ｐ，ｓ＞０，使得．（２）设Ｒ为半局部Ｄｅｄｅｋｉｎｄ环，Ｇ为有限生成Ａｂｅｌ群，则Ｋ＿０ＲＧ为挠群ｉｆｆ如果Ｇ有素数ｐ阶元，则（３）如果Ｋ＿０ＲＧ为挠群，［Ｇ∶Ｈ］＜∞，则对任何，有．这里Ｒ为整环，Ｌ为其分式域。 In this paper, we introduce the field of fractiows on integaralring F CxD .discuss the integral division problem for Polynomials of two elements and prove the existence of maximum common factor for Polynomials, give a method for maximum. Common factor of Polynomials of two elements. 在整环F(x)的分式域上,讨论了二元多项式的整除问题,论证了二元多项式最大公因式的存在性及求法。 In this paper,the group of automorphisms of a class of Witt type Lie algebras and the group of automorphisms of the corresponding commutative associative algebras are realted.As a consequence,the following result is proved.Let F be a field of characteristic 0, t -1,t -2,…,t -n be n commuting variables over F,F(t -1,t -2,…,t -n) be the field of all rational functions.Let D=n i=1 F  t -i .We have the simple Witt type Lie algebra F(t -1,t -2,…,t -n)D. Then Aut (F(t -1,t... In this paper,the group of automorphisms of a class of Witt type Lie algebras and the group of automorphisms of the corresponding commutative associative algebras are realted.As a consequence,the following result is proved.Let F be a field of characteristic 0, t -1,t -2,…,t -n be n commuting variables over F,F(t -1,t -2,…,t -n) be the field of all rational functions.Let D=n i=1 F  t -i .We have the simple Witt type Lie algebra F(t -1,t -2,…,t -n)D. Then Aut (F(t -1,t -2,…,t -n)D)Aut(F(t -1,t -2,…,t -n)). 研究了一类Witt型李代数自同构群和其相关的交换结合代数的自同构群 ,得到如下结果 :设F为一个特征为0的域 ,t1 ,t=- 2 ,… ,tn 为F上几个交换的变元 ,F(t1 ,t2 ,…tn)表示t1 ,t2 ,… ,tn 生成的分式域 ,令D = ni=1 F ti,则得到一类witt单李代数且有Aut(F(t1 ,t2 ,… ,tn)D) Aut(F(t1 ,t2 ,… ,tn) ) .
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