Localization of a ring

So what exactly is the localization of a ring? It is creating a field-imitation (and NOT necessarily a field with multiplicative inverses) for every ring. It includes the creation of multiplicative inverse- imitations (for elements that are not zero-divisors). How does it do this? It apes the steps taken to create a field of fractionsContinue reading “Localization of a ring”

I’ve always found the construction of the quotient field of a domain very arduous and time-consuming. Most people get lost somewhere in the proof. I am going to try and make it more transparent. What are we trying to do? We’re trying to convert a ring into a field (please forgive my language). How areContinue reading