设S是复数集的非空子集。如果S中的数对任意两个数的和、差、积仍属于S，则称S是一个数环。例如整数集Z就是一个数环，有理数集Q、实数集R、复数集C等都是数环。 由于有理数集Q、实数集R、复数集C有更好的性质，所以他们还是数域。
整数环 [数] ring of integers ; integer ring
幂级数环 [数] power series ring ; the ring of power series ; formal series rings
形式幂级数环 [数] ring of formal power series ; [数] formal power series ring
系数环 [数] coefficient ring
有理整数环 [数] ring of rational integers
代数环 Algebraic loop
四元数环 [数] quaternion ring ; [数] ring of quaternions
计数环 counting ring
收敛幂级数环 [数] ring of convergent power series ; [数] convergent power series ring
尽管凯斯·希勒全国房价指数及十大城市综合指数与去年相比有所上扬，但是截止到三月末的连续三个月这一指数环比连续下挫。
Although both the Case-Shiller national and ten-city indices are up year-on-year, the national index fell during the three months to the end of March.
利用数域上一元多项式环与整数环相似的性质，建立数域上一元多项式环中的孙子定理，并给出它的简单应用。
Using the similarity between polynomial ring and integer ring the paper establishes Sunse's Theorem in the polynomial ring in number field, and offers its brief learning and practice.
证明了任一环有代数封闭的扩张环，且实封闭域上的四元数体是代数封闭的，给出了代数封闭环的若干性质。
The two theorems are proved that any ring can be extended into an algebraically closed ring and that the quaternionic skew field over a real closed field is algebraically closed.
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