**<The Detail of This Chapter.pdf>**

(R, +) is a Abel group;

(R, *) is a semi-group;

(+, *) satisfy distributive law;

then (R, +, *) is a ring.

<if * holds commutativity, R is a commutative ring; if (R, *) is a unity semi-group, R is a unity ring.>

from the distributive law, we can get the relationship of + and *.