1.Since the identity element of a monoid is unique, one can alternately define the identity function on M to be this identity element.
因为么半群的单位元是唯一的，可以以M上的单位元来替代其恒等函数的定义。
2.In this paper, the join of two trees with a regular monoid is explicitly described.
明确给出了具有正则自同态幺半群的两个树的联。
3.A non-trivial ring is prime if and only if the monoid of its ideals lacks zero pisors.
一个非零环是素环当且仅当其双边理想在乘法下构成的幺半群无零因子。
4.From here on out, the term " monoid" will be used.
此后就使用术语“幺半群”。
5.The Structure of the Endomorphism Monoid of a Graph
图半群的结构
6.Some results on inversity of endomorphism monoid of generalized join
广义联图的自同态幺半群的可逆性的一些结果