GATE 2021 MA – Question 28

Algebra · Rings and Ideals · 1 mark · Numerical answer

Let I=(x²+x+1) in R=ℤ₃[x]. Find the number of units in R/I.

Show answer and explanation

Correct answer: 6 to 6

Explanation

Over 𝔽₃, x²+x+1=(x−1)². The quotient is 𝔽₃[ε]/(ε²), with 9 elements a+bε. It is a unit precisely when a≠0, giving 2×3=**6** units.

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