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- Let D_(l+1)(R) be the orthogonal Lie algebra over a commutative ring R with 2 invertible and m_1 an l+ 1 upper triangular matrix. 設D_(l+1)(R)表示2為單位交換環R上的2(l+1)階正交李代數。 若記m_1是R上的l+1階三角矩陣，而是D_(l+1)(R)可解子代數。
- A commutative ring with unity having no proper divisors of zero, that is, where the product of nonzero elements cannot be zero. 整環，整域：一個單位元素都不是零的真約數，即，非零元素的乘積不為零的交換環
- Let R be a commutative ring without zero-divisor,R is called a quasi-valuation ring,if it contains a non-zero element a such that any non-zero element of R divides a power of a. 一個無零因子的交換環R稱為擬賦值環,如果R中有一個非零元素a,使得R的任意非零元都整除a的某個方冪。
- The fundamental theorem of arithmetic is an important and basic theorem of theory of number and plays an important role in modern commutative ring theory. 算術基本定理是初等數論中一條非常基本和重要的定理,它所體現的唯一因子分解的思想,在現代交換環理論中起著非常重要的作用。
- See invertible matrix for more.More generally, a square matrix over a commutative ring R is invertible if and only if its determinant is invertible in R. 更一般地，一元素在一可交換環R內的方陣是可逆的若且唯若其行列式在R是可逆的。
- She had the sapphire set in a gold ring. 她把那枚藍寶石鑲在金戒指上了。
- The diamond ring dazzled with brilliancy. 這隻鑽石戒指閃耀奪目。
- L_Z associated with finite-dimensional simpleLie algebras and affine Lie algebras of type k =1 over a commutative ring withidentity were defined by J. Hurley in 1969 and 1981 respectively, and theirideal structures were worked out there. Hurley在1969年與1981年分別對有限維復單李代數及k=1的仿射李代數L研究了相應的Chevalley代數L_R=RL_z的理想結構。
- She wears a diamond ring on her left hand. 她左手上戴著一枚鑽石戒指。
- Our family reunions are always three ring circus. 我家合家團聚的場面總是熱鬧非凡。
- I am sorry-she's out. Can you ring again later? 對不起－她出去了。你過些時候再打電話來好嗎？
- The boys and girls made a ring round us. 男孩和女孩圍著我們站了一圈。
- Many people know mathematics, at least they know commutative rings when they are married. 其實很多人都會數學，最少在他們結婚的時候會交換戒指。
- Please ring for the attendant if you need anything. 如果需要什麼，請按鈴找服務員。
- In this paper, we study the subalgebra structure of the general linear Lie algebras over commutative rings. 摘要本文研究了含幺可換環上一般線性李代數的子代數結構。
- The music was so loud it made my ears ring. 音樂的聲音太大了，把我耳朵震得直響。
- Commutation is distinct from reprieve. 減刑不同於緩刑。
- The policeman felt that my story didn't ring true. 警察認為我講的話聽起來不可信。
- She wears a ring round her wrist. 她的手腕上戴著一隻鐲子。
- He appealed for (a) commutation of the death sentence to life imprisonment. 他已上訴請求將死刑減為無期徒刑。
