Obtaining injective modules with Singular
Questionn ยท Wed Sep 16, 2020 11:23 pm
Hi,
I have not used singular before but read a bit in the book, but was not able to find the commands needed to produce indecomposable injective modules in a given commutative ring.
Given a ring R, any such indecomposable injective module is isomorphic to the injective envelope of a module of the form R/p for a prime ideal p. So the input is a ring R together with a prime ideal p and the output should be the injective envelope of the module R/p. How can this be done with singular?
For example one could take R to be the polynomial ring in two variables over the complex numbers and for p a prime ideal generated by some polynomials.
Thank you for the help
I have not used singular before but read a bit in the book, but was not able to find the commands needed to produce indecomposable injective modules in a given commutative ring.
Given a ring R, any such indecomposable injective module is isomorphic to the injective envelope of a module of the form R/p for a prime ideal p. So the input is a ring R together with a prime ideal p and the output should be the injective envelope of the module R/p. How can this be done with singular?
For example one could take R to be the polynomial ring in two variables over the complex numbers and for p a prime ideal generated by some polynomials.
Thank you for the help