PRIME AND MAXIMAL IDEALS For all parts below, assume R is a commutative ring with 1. DEFINITION: We define an ideal I C R to be a prime ideal if it is a proper ideal of R with the property that whenever ab E I we have either a E I or b E I. CLAIM: If p e Z with p > 2 then (p) is a prime ideal if and only if p is a prime number.

PRIME AND MAXIMAL IDEALS For all parts below, assume R is a commutative ring with 1. DEFINITION: We define an ideal I C R to be a prime ideal if it is a proper ideal of R with the property that whenever ab E I we have either a E I or b E I. CLAIM: If p e Z with p > 2 then (p) is a prime ideal if and only if p is a prime number.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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PRIME AND MAXIMAL IDEALS
For all parts below, assume R is a commutative ring with 1.
DEFINITION: We define an ideal I C R to be a prime ideal if it is a proper ideal of R with the
property that whenever ab E I we have either a E I or b E I.
CLAIM:
If p e Z with p > 2 then (p) is a prime ideal if and only if p is a prime number.

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