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how to check maximal ideals in ring of two variables

asked 2021-10-07 01:37:12 +0200

P_Singh gravatar image

updated 2021-10-07 10:54:32 +0200

tmonteil gravatar image

When I tried the following:

R.<x, y>= QQ[ ]
I= R.ideal([x, y])
I.is_prime()
I.is_maximal()

It is running true for I.is_prime but there is an error message when I am running I.is_maximal. It is happening for ring of integers as well. For ring of univariate polynomials, the same command is not giving any error.

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answered 2021-10-07 11:02:20 +0200

tmonteil gravatar image

Indeed, it seems not implemented (the returned error is ImplementedError).

If you look at the code of the is_maximal method:

sage: I.is_maximal??

you will see that the difference is that for univariate polynomial rings, the Krull dimension is 1, while here it is 2.

If you know some method to decide such maximality, it could be added to Sage source code.

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Asked: 2021-10-07 01:37:12 +0200

Seen: 24 times

Last updated: Oct 07