(... On Tuesday, June 12, 2007 I wrote:

Let I, J be ideals of Z.

If I=(m), J=(n) then I+J=(GCD(m,n)), and I∩J=(LCM(m,n)). ...)

In fact:

Let I, J be ideals of Z.

If I=(m), J=(n) then

- I*J=(m*n)

- I+J=(GCD(m,n)),

- I∩J=(LCM(m,n)),

- I∪J=I+J.

Example:

I = (6) = {..., -18, -12, -6, 0, 6, 12, 18, 24, ...}

J = (4) = {..., -12, -8, -4, 0, 4, 8, 12, 16, ...}

- I*J={..., -48, -24, 0, 24, 48, 72, ...}

- I+J=(GCD(m,n))={..., -4, -2, 0, 2, 4, 6, ...},

- I∩J=(LCM(m,n))={..., -24, -12, 0, 12, 24, 36, ...},

- I∪J=I+J={..., -4, -2, 0, 2, 4, 6, ...}.

2-2018 Teaching by misleading

2 months ago

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