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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:...
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:...
Each field of characteristic zero contains a copy of the rational number field
Solution to Linear Algebra Hoffman & Kunze Chapter 1.2 Exercise 1.2.8 Solution: Call the additiv...
Each subfield of the field of complex numbers contains every rational number
Solution to Linear Algebra Hoffman & Kunze Chapter 1.2 Exercise 1.2.7 Solution: Every subfield o...
Verify the set with addition and multiplication is a field
Solution to Linear Algebra Hoffman & Kunze Chapter 1.2 Exercise 1.2.5 Solution: We must check th...
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: ...
In a unital ring, if the quotient corresponding to an ideal is a field, then the ideal is maximal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.5 Solution: ...
A commutative unital ring is a field precisely when the zero ideal is maximal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.4 Solution: ...
Verify that the set of complex numbers is a subfield of C
Solution to Linear Algebra Hoffman & Kunze Chapter 1.2 Exercise 1.2.1 Solution: Let $F=\{x+y\sqr...