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location Singapore
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visits member for 2 years, 10 months
seen 10 hours ago

C'est par la logique qu'on démontre, c'est par l'intuition qu'on invente.


Jan
21
comment For a non-unit element $x$ in a unital ring, does non-zero $a$ or $b$ ALWAYS exist s.t. $ax=xb=0$?
Yes I'm looking for non-zero $a$ and $b$. just updated the question. Thanks for the hint "the simplest example Z". Why, for example if $x=7$, there's no $a$ or $b$ so that $a7=7b=0$. It's so blatant!
Jan
21
revised For a non-unit element $x$ in a unital ring, does non-zero $a$ or $b$ ALWAYS exist s.t. $ax=xb=0$?
added 9 characters in body; edited title
Jan
21
accepted Is it always possible to extend a ring to a unital ring?
Jan
21
comment For a non-unit element $x$ in a unital ring, does non-zero $a$ or $b$ ALWAYS exist s.t. $ax=xb=0$?
@fundamental i've updated the question.
Jan
21
comment For a non-unit element $x$ in a unital ring, does non-zero $a$ or $b$ ALWAYS exist s.t. $ax=xb=0$?
sorry my intention is to ask if such $a$ and $b$ always exist, for all $x$. I've updated the question.
Jan
21
revised For a non-unit element $x$ in a unital ring, does non-zero $a$ or $b$ ALWAYS exist s.t. $ax=xb=0$?
deleted 53 characters in body; edited title
Jan
21
awarded  Custodian
Jan
21
reviewed Approve For a non-unit element $x$ in a unital ring, does non-zero $a$ or $b$ ALWAYS exist s.t. $ax=xb=0$?
Jan
21
asked For a non-unit element $x$ in a unital ring, does non-zero $a$ or $b$ ALWAYS exist s.t. $ax=xb=0$?
Jan
21
asked Is it always possible to extend a ring to a unital ring?
Jan
17
accepted Given a finite set, how to generate all possible groups defined on it?
Jan
17
comment Given a finite set, how to generate all possible groups defined on it?
thanks a lot! It's quite detailed introduction. I'm bookmark it so will come back reviewing topics like Sylow Theorems, simple groups etc. Once again thanks your time!
Jan
17
comment Given a finite set, how to generate all possible groups defined on it?
@Travis thanks for the sequence. so now we have the counts. is there somewhere listing out the groups? or it's a trivial question that people don't normally list out the groups for study? (Maybe mathematicians study the patterns?) For fixing the identity elements, I was thinking there's always an identity, so switching the elements do not change the "pattern" or "structure" of the group...
Jan
17
comment Given a finite set, how to generate all possible groups defined on it?
@oldrinb is there a website or something listing the possible groups for some initial $n$s, say $n<10$?
Jan
17
asked Given a finite set, how to generate all possible groups defined on it?
Jan
11
comment How to prove tr AB = tr BA?
@hihihi57 right... i should have thought that...
Jan
11
comment How to prove tr AB = tr BA?
amazing... they have the same characteristic polynomial? how to show that ?
Jan
11
accepted How to prove tr AB = tr BA?
Jan
11
asked How to prove tr AB = tr BA?
Dec
19
comment math books of undergraduate/graduate level without formula?
@RossMillikan exactly. So I just wonder if anyone got a try? something like an economics book without a diagram ... or "A Brief History of Time" by Stephen Hawking on physics.