Rings and Fields

Which of the following is a commutative ring without unity

• Z

• 3Z

• Z₃

• M₂(Z)

Every non zero element in Z_n is

• a zero divisor

• a unit

• either a zero divisor or a unit

• Neither a zero divisor nor a unit

Let A be a subring of a commutative ring R such that for every r in R and for every a in A , ra is in A then A is called

• Ideal

• Field

• Integral domain

• Factor ring

Identify maximal ideal of Z₃₆

• <4>

• <3>

• <12>

• <9>

R be a commutative ring with unity and let A be a an ideal of R. Which of the following is not true

• R/A is an integral domain if A is maximal

• R/A is an integral domain if A is prime

• A is prime if R/A is an integral domain

• R/A is a field if A is maximal

Which of the following is a homomorphism from Z to Z_m

• n to mn

• n to n(mod m)

• n to m

• n to n+m

Which of the correspondence from Z₄ to Z₁₂ does not preserve multiplication

• x to x

• x to 3x

• x to 0

• x to 1

Units of Z are

• 0 and 1

• 1 and -1

• -1 and 0

• -1, 0 and 1

Tags

CCSS.8.EE.C.7B

Which of the following is true

• Every ring is a field

• Every finite integral domain is a field

• Every integral domain is a field

• Every ideal is prime ideal

Let f (x) ∈ Z[x]. If f (x) is reducible over Q, then

• f(x) is reducible over Z

• f(x) is irreducible over Z

• f(x) is irreducible over R

• f(x) is irreducible over C

Tags

CCSS.HSF-IF.C.7C