基本的运算法则已经形成，包括加法运算、数乘运算、加法的消去律等。
Basic operation rules have been established, including addition, positive scalar multiplication, cancellation law for addition and so on.
我们容易验证乘法满足结合律和交换律，并且由加法结果的唯一性得出乘法结果的唯一性和乘法消去律。
We then can verify the associative law and the commutative law for multiplication, and the uniqueness of the result of addition indicates the uniqueness and the cancellation law for multiplication.
本文证明了任意一个I 半群不满足消去律，而且满足消去律的半群的所有真双理想不可能同时都是群。
This (paper) showed that an arbitrary I-semigroup is not satisfied with cancellation law and all real-bi-ideal of semigroup satisfied with cancellation law can not be I-semigroups at the same time.
这里我们用到了乘法结合律也可以用消去律，本来这些运算律是对正整数乘法适用的，但对于有分数参加的乘法我们也规定适用。
Here we have used the associative law or the cancellation law for multiplication, which are satisfied for natural Numbers, now we assume they are satisfied with fraction Numbers.
这里我们用到了乘法结合律也可以用消去律，本来这些运算律是对正整数乘法适用的，但对于有分数参加的乘法我们也规定适用。
Here we have used the associative law or the cancellation law for multiplication, which are satisfied for natural Numbers, now we assume they are satisfied with fraction Numbers.
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