Let P be a prime ideal in a commutative ring R and let S = R\P, i.e. the complement of P in R. Pick out the true statements: (a) S is closed under addition. (b) S is closed under multiplication. (c) S is closed under addition and multiplication
a question on complement of prime ideal
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abstract-algebra
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0Can you tell us your thoughts on the problem? – 2012-09-19
1 Answers
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(a) is false(e.g. $\mathbb{Z} - 2\mathbb{Z}$).
(b) is true.
(c) is false, since (a) is false.