More Abstract Algebra!
I have not posted in a while, but I have some more questions:
1. Can someone come up with an example of a ring with unity and no zero divisors that is not an integral domain? I know I need an example that meets the first two criteria but is not commutative... but I cannot come up with one. Any takers?
2. Given D = integral domain and S={n*1 | n in Z} where 1 = unity in D, I need to show that if R is any subdomain of D, then S is a subset of R. Well, I can easily show that S is a subdomain of D.... but I'm not sure how to show that S is a subset of any such R. Ideas for me?
3. What are all the subdomains of Z? I know nZ is not a subdomain except n=1 since then it would not have unity=1, but I don't know what the subdomains are... Ideas for me?
4. I need to show that the only subdomain of Zp (where p=prime) is Zp. Again, I have no idea where to start.
Thanks... as usual.
Ciao.
1. Can someone come up with an example of a ring with unity and no zero divisors that is not an integral domain? I know I need an example that meets the first two criteria but is not commutative... but I cannot come up with one. Any takers?
2. Given D = integral domain and S={n*1 | n in Z} where 1 = unity in D, I need to show that if R is any subdomain of D, then S is a subset of R. Well, I can easily show that S is a subdomain of D.... but I'm not sure how to show that S is a subset of any such R. Ideas for me?
3. What are all the subdomains of Z? I know nZ is not a subdomain except n=1 since then it would not have unity=1, but I don't know what the subdomains are... Ideas for me?
4. I need to show that the only subdomain of Zp (where p=prime) is Zp. Again, I have no idea where to start.
Thanks... as usual.
Ciao.