Polynomial Ring10

Compute in a quotient of a polynomial ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.16 Solution:...
Basic properties of quotients of a polynomial ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.14 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: ...
Compute the powers of a given ideal in a polynomial ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.36 Solution:...
Characterize the units and nilpotent elements of a polynomial ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.33 Solution:...
Decide whether or not a subset of Z[x] is a subring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.10 Solution:...
Z[x] and Q[x] are not isomorphic
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.2 Prove that...
Compute some orbits of an action by Sym(4) on polynomials in four variables
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.6 As in Exer...
Characterization of zero divisors in a polynomial ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.2 Let $R$ be...
Compute in a polynomial ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.1 Let $p(x) ...