1. ## quotient Rings 1

Let R be a ring: since R is an abelian group under +, na has meaning for us for n in Z, a in R. Show that (na)(mb)=(nm)(ab) if n,m are integers and a,b in R.

2. Originally Posted by mpryal
Let R be a ring: since R is an abelian group under +, na has meaning for us for n in Z, a in R. Show that (na)(mb)=(nm)(ab) if n,m are integers and a,b in R.

$(na)(mb) = \underbrace{(a + a + \cdots + a)}_{n \text{ times}} \underbrace{(b + b + \cdots + b)}_{m \text{ times}} = \cdots$