Integral Domain12

Every prime ideal in a Boolean ring is maximal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.23 Solution:...
A finite unital ring with no zero divisors is a field
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.21 Solution:...
The ideal generated by the variable is maximal iff the coefficient ring is a field
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.18 Solution:...
Prove that a given quotient ring is not an integral domain
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.17 Solution:...
If a nontrivial prime ideal contains no zero divisors, then the ring is an integral domain
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.10 Solution:...
In an integral domain, two principal ideals are equal precisely when their generators are associates
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.8 Solution: ...
In a polynomial ring, the ideal generated by the indeterminate is prime precisely when the coefficient ring is an integral domain
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.7 Solution: ...
The characteristic of an integral domain is prime or zero
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.28 Solution:...
The ring of formal power series over an integral domain is an integral domain
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.4 Prove that...
The only Boolean integral domain is Z/(2)
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.16 Prove tha...