1. His classmates were labouring with elementary algebra.
   他的同学们正在绞尽脑汁地演算初等代数题。
2. He was not good at algebra in middle school.
   他中学时不擅长代数。
3. In algebra, the sign X usually denotes an unknown quantity.
   在代数里, 符号X常用来表示未知数。
4. Four years after he graduated from school, Tom decided to dust off his algebra book.
   汤姆从学校毕业四年后, 决意重温代数。
5. Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of its exact Borel subalgebras.
   【摘要】： 正 It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other.
6. If you want to be a draftsman, a machinist, a molder, or a patternmaker, you'll need algebra and geometry and even trigonometry.
   如果你想成为手工艺人、缝纫工、造型工或制模工，你需要代数和几何，甚至三角学。
7. Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.
   在复平面C中，任意有界域的拓扑边界上连续函数代数的K_1-群与其边界上的上同伦群同构。
8. Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.
   利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。
9. In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.
   本文中，我们证明了作为泛代数的半格的定义与作为偏序集的半格的定义是等价的。
10. In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.
    文章通过李子群的性质得出了李群的两个李子群的交依然是李子群的结论,进而得出这一李子群的李代数形式。

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