Prove that K is not equal to IJ

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Im not sure how to prove this. Maybe i can show that IJ is bigger than K, and show a counter example where something is in IJ but not in K? but not sure how to do this either.

asked Nov 19 at 0:52

H.B

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up vote
-2
down vote

favorite

enter image description here

Im not sure how to prove this. Maybe i can show that IJ is bigger than K, and show a counter example where something is in IJ but not in K? but not sure how to do this either.

asked Nov 19 at 0:52

H.B

203

add a comment |

up vote
-2
down vote

favorite

enter image description here

Im not sure how to prove this. Maybe i can show that IJ is bigger than K, and show a counter example where something is in IJ but not in K? but not sure how to do this either.

asked Nov 19 at 0:52

H.B

203

enter image description here

Im not sure how to prove this. Maybe i can show that IJ is bigger than K, and show a counter example where something is in IJ but not in K? but not sure how to do this either.

abstract-algebra polynomials ideals

asked Nov 19 at 0:52

H.B

203

asked Nov 19 at 0:52

H.B

203

asked Nov 19 at 0:52

H.B

203

asked Nov 19 at 0:52

H.B

203

asked Nov 19 at 0:52

H.B

203

add a comment |

1 Answer
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Hint:

For example, $;p(x)=4x^2+2xin IJ;$ , yet $;p(x)notin K;$ . Try to prove this.

answered Nov 19 at 0:57

DonAntonio

176k1491224

But aren't the polynomials in I zero?
– H.B
Nov 19 at 1:06

@H.B What? The polynomials in $;I;$ are all those polynomials that vanish at zero, not only the zero polynomial...
– DonAntonio
Nov 19 at 1:07

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

up vote
0
down vote

Hint:

For example, $;p(x)=4x^2+2xin IJ;$ , yet $;p(x)notin K;$ . Try to prove this.

answered Nov 19 at 0:57

DonAntonio

176k1491224

But aren't the polynomials in I zero?
– H.B
Nov 19 at 1:06

@H.B What? The polynomials in $;I;$ are all those polynomials that vanish at zero, not only the zero polynomial...
– DonAntonio
Nov 19 at 1:07

add a comment |

up vote
0
down vote

Hint:

For example, $;p(x)=4x^2+2xin IJ;$ , yet $;p(x)notin K;$ . Try to prove this.

answered Nov 19 at 0:57

DonAntonio

176k1491224

But aren't the polynomials in I zero?
– H.B
Nov 19 at 1:06

@H.B What? The polynomials in $;I;$ are all those polynomials that vanish at zero, not only the zero polynomial...
– DonAntonio
Nov 19 at 1:07

add a comment |

up vote
0
down vote

Hint:

For example, $;p(x)=4x^2+2xin IJ;$ , yet $;p(x)notin K;$ . Try to prove this.

answered Nov 19 at 0:57

DonAntonio

176k1491224

Hint:

For example, $;p(x)=4x^2+2xin IJ;$ , yet $;p(x)notin K;$ . Try to prove this.

answered Nov 19 at 0:57

DonAntonio

176k1491224

answered Nov 19 at 0:57

DonAntonio

176k1491224

answered Nov 19 at 0:57

DonAntonio

176k1491224

answered Nov 19 at 0:57

DonAntonio

176k1491224

But aren't the polynomials in I zero?
– H.B
Nov 19 at 1:06

@H.B What? The polynomials in $;I;$ are all those polynomials that vanish at zero, not only the zero polynomial...
– DonAntonio
Nov 19 at 1:07

add a comment |

But aren't the polynomials in I zero?
– H.B
Nov 19 at 1:06

@H.B What? The polynomials in $;I;$ are all those polynomials that vanish at zero, not only the zero polynomial...
– DonAntonio
Nov 19 at 1:07

But aren't the polynomials in I zero?
– H.B
Nov 19 at 1:06

@H.B What? The polynomials in $;I;$ are all those polynomials that vanish at zero, not only the zero polynomial...
– DonAntonio
Nov 19 at 1:07

add a comment |

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