Rings and Fields
Description: This quiz covers the fundamental concepts and properties of rings and fields, which are essential algebraic structures in abstract algebra. | |
Number of Questions: 15 | |
Created by: Aliensbrain Bot | |
Tags: rings fields algebraic structures abstract algebra |
Which of the following is a commutative ring with unity?
What is the multiplicative inverse of 3 in the field (ℤ/5ℤ, +, ×)?
Which of the following is a field?
What is the characteristic of the field (𝔽_5, +, ×)?
Which of the following is an ideal of the ring (ℤ, +, ×)?
What is the maximal ideal of the ring (ℤ, +, ×)?
Which of the following is a principal ideal domain?
What is the unity element of the ring (ℤ/6ℤ, +, ×)?
Which of the following is a field extension of the field (ℚ, +, ×)?
What is the degree of the field extension (ℚ(√2), +, ×) over (ℚ, +, ×)?
Which of the following is a Galois field?
What is the order of the Galois field (ℤ/7ℤ, +, ×)?
Which of the following is a polynomial ring over the field (ℤ/2ℤ, +, ×)?
What is the degree of the polynomial x^3 + x + 1 in the polynomial ring (ℤ/2ℤ[x], +, ×)?
Which of the following is a maximal ideal of the polynomial ring (ℤ/2ℤ[x], +, ×)?