I am trying to use MAGMA to find the set of zero divisors of the 2x2 matrix algebra. From what I have researched, there is no straightforward command, so I attempted to use some simple "for" statements to coax out the answer:
Code: Select all
> T:=MatrixAlgebra< GF(2), 2 |>;
> for i in T do
for> for j in T do
for|for> i*j;
for|for> if i*j eq 0 then
for|for|if> print i;
for|for|if> print j;
for|for|if> end if;
for|for> end for;
for> end for;
[0 0]
[0 0]
[0 0]
[0 0]
[0 0]
[0 0]
Clearly, this was unsuccessful, as the program yielded only trivial zero divisors. I re-ran the code with slightly different phrasing, solving for i when Determinant(i) eq 0, but the results were identical. I'm wondering what exactly I'm doing wrong, or if I'm going about this the wrong way. Is there some more effective strategy?