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2h
comment Simultaneously vanishing quadratic forms?
Conceptually you're just checking the intersection of the radicals of the forms... but I guess that isn't concrete enough?
3h
awarded  Enlightened
4h
awarded  Nice Answer
6h
comment Lattices and Hasse diagrams
@JavierArias It can be problematic to do a Hasse diagram for infinite sets. You can see that here for example. You can generate a Hasse diagram for any finite poset.
6h
revised Lattices and Hasse diagrams
added 54 characters in body
6h
comment Lattices and Hasse diagrams
@GitGud Good comparison :)
6h
answered Lattices and Hasse diagrams
6h
revised Is ideal an “anti-field”?
added 189 characters in body
7h
comment Is ideal an “anti-field”?
@A.Magnus added one more paragraph about the noncommutative ring situation.
7h
revised Is ideal an “anti-field”?
added 328 characters in body
9h
comment Ideals of non semi-simple group rings.
It's not semisimple, but it is still quasi-Frobenius. Since I'm not super comfortable with semidirect products, my intuition about the structure breaks down a bit. You might be able to compute directly what its central idempotents are, and therefore come to the conclusion that it splits as Derek described. I'd hope that'd give some members of your chain, and maybe by then you'd see some dimensionality fact that would help you sort out if your chain is maximal or not.
9h
comment Ideals of non semi-simple group rings.
Dear Derek : That's really cool! It's a great tragedy in my life that I've never had the time to pick up Magma. Might you be willing to share the code you used somehow? Perhaps as a gist? Regards
9h
revised Is ideal an “anti-field”?
added 19 characters in body
9h
answered Is ideal an “anti-field”?
9h
comment Some doubts about right ideals of a ring
A fortiori, the axioms of ring multiplication allow you to conclude $R$ is a right $R$ module with the ring multiplication as the action. That right ideals are the same thing as right submodules follows directly from the definitions. And finally yes, the quotient being a ring necessitates $T$ being a two-sided ideal. Is there any question left?
1d
revised Difference between torsion and zero divisor
added 88 characters in body
1d
comment Difference between torsion and zero divisor
I get the feeling you didn't read the definitions very carefully: how could they be considered the same? They're of a similar flavor, of course... but the definitions aren't identical...
1d
answered Difference between torsion and zero divisor
1d
comment Proof about the difference between right and left ideals in a ring
@JavierArias I think someone has already pointed out to you in your proof that if the $R$ in the proof is commutative, it will be proving a commutative ring has a left ideal that isn't a right ideal, which is absurd. The strategy of beginning with "Let $M$ be a module over a ring $R$..." and then proving not all left ideals are right ideals is doomed to failure for that reason.
1d
comment Proof about the difference between right and left ideals in a ring
@JavierArias Of course it could be trying to explain heuristically why it is not the case, but that is not really a formal proof. Similarly if you had the statement "aliens don't exist" and you wanted to show that this statement is wrong, then you can wave your hands all day with axioms showing that they could possibly exist, but that isn't convincing. What would really be convincing is to produce an alien as a counterexample to the claim.