I am trying to solve Abstract Algebra of David S. Dummit & Richard M. Foote. Almost most of the problems are statement proving type. But now I have found some counting, precisely speaking numerical answer type questions such as find out the number of prime ideals of the given ring etc. There are millions of problems of this book which are still unsolved by me. So I need a answer key to verify my work ,specialy numerical answer type questions. I have searched in Google but what I get is very naive and solved very few problems. Please provide me any accessible link of answer key , Now I am doing exercise 9.2 , so for now it's enough to get 9.2 answer key only if the whole answer key is currently unavailable.
Thanks for reading!
1) Looks like ${\Bbb Z}_2[x,y]/\langle x^2,y^2\rangle$ with generating set $1,x,y,xy$.
2) Hint: The ideals of ${\Bbb Z}_2[x]/\langle x^3+1\rangle$ are in one-to-one correspondence with the ideals of ${\Bbb Z}_2[x]$ containing $\langle x^3+1\rangle$ (by one of the isomorphism theorems for rings).