Commutative Ring20

The set of prime ideals of a commutative ring contains inclusion-minimal elements
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.36 Solution:...
Definition and basic properties of the Jacobson radical of an ideal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.32 Solution:...
In a commutative ring, prime ideals are radical
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.31 Solution:...
Definition and basic properties of the radical of an ideal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.30 Solution:...
An ideal which is finitely generated by nilpotent elements is nilpotent
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.28 Solution:...
Constructing units from nilpotent elements in a commutative ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.27 Solution:...
The nilradical of a commutative ring is contained in every prime ideal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.26 Solution:...
A sufficient condition for the ring property that every prime ideal is maximal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.25 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:...
A nonzero finite commutative ring with no zero divisors is a field
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.20 Solution:...