# quotient Rings 1

• Apr 24th 2009, 12:24 PM
mpryal
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.

Please show steps. Thanks!
• Apr 24th 2009, 12:33 PM
Jhevon
Quote:

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.

Please show steps. Thanks!

you've posted a lot of questions, i can't help but think you want us to do your homework for you :p

anyway, use what na and mb means...

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

what does this have to do with quotient rings?