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Topic review  homomorphisms between modules 
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homomorphisms between modules 


we would like to calculate Hom_R(I,R/I) for a polynomial ring R and an ideal I in R. according to the description in the online manual this is done by representing I and R/I as cokernel of matrices B and A by asking for "Hom(B,A)". these matrices are obtained by taking a free resolution of R/I as
R^p B> R^q A> R > R/I
but the output of "Hom(B,A)" is an object of SINGULAR data type "module", which is, if we understand correctly, a submodule of a free module (of rank 324 in our example btw..) but this cannot be Hom_R(I,R/I), which is a torsion module.
1) how do we have to interpret "Hom(B,A)? 2) how do we obtain the module Hom_R(I,R/I) we are looking for?
thanks
we would like to calculate Hom_R(I,R/I) for a polynomial ring R and an ideal I in R. according to the description in the online manual this is done by representing I and R/I as cokernel of matrices B and A by asking for "Hom(B,A)". these matrices are obtained by taking a free resolution of R/I as
R^p B> R^q A> R > R/I
but the output of "Hom(B,A)" is an object of SINGULAR data type "module", which is, if we understand correctly, a submodule of a free module (of rank 324 in our example btw..) but this cannot be Hom_R(I,R/I), which is a torsion module.
1) how do we have to interpret "Hom(B,A)? 2) how do we obtain the module Hom_R(I,R/I) we are looking for?
thanks




Posted: Wed Jan 30, 2013 12:50 am 





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