"Suppose that R is a commutative ring and..." was answered by our community

College
Algebra
Abstract algebra

Answered question

2022-04-10

Suppose that R is a commutative ring and |R| = 30. If I is an ideal of R and |I| = 10, prove that I is a maximal ideal

Answer & Explanation

star233

Skilled2022-06-09Added 403 answers

Recall that an ideal is maximal if and only if the quotient ring is a field. Here, $R / I$ is a ring with $| R | / | I | = 30 / 10 = 3$ elements, and is thus a field. It follow that $I$ is maximal.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Abstract algebra

How to find out the mirror image of a point?
Generators of a free group
If G is a free group generated by n elements, is it possible to find an isomorphism of G with a free group generated by n-1 (or any fewer number) of elements?
How many 3/4 Are in 1
Convert 10 meters to feet. Round your answer to the nearest tenth
6. Reduce the following matrix to reduced row echelon form:
$C equals open parentheses table row 1 cell negative 1 end cell cell 1 half end cell cell 1 half end cell row 0 1 cell 1 half end cell cell negative 1 half end cell row 0 0 1 0 row 0 0 0 0 end table close parentheses$
Let v be a vector over a field F with zero vector 0 and let s,T be a substance of V .then which of the following statements are false
Describe Aut(Zp), the automorphism group of the cyclic group Zp where p is prime. In particular find the order of this group. (Hint: A generator must map to another generator)

Didn't find what you were looking for?