Study for Ring of Quotients and Multiplicative Subset

Abstract

The research and development of natural science must rely on mathematics, and important branch of mathematics are algebra, ring as the basic content of algebra played an extremely important role in the development of algebra. In this paper, we study rings of quotients and localization. The first multiplicative provided and the concept of ring of quotients are defined, then on the commutative ring and the multiplicative subset defines a equivalence relation, the equivalence relation has carried on the thorough research, there several theorems are proved, and finally got the conclusion: a multiplicative subset of a commutative ring can always homomorphism to embedded in any commutative ring with the identify.