Are musicians usually this dumb?

[fftransform]

okay, since you've completely degraded yourself to childish insults. I'll leave you at that.
 
I was hoping you would jump into the fray cause you've confessed to a phd degree in math.

He knows more math than you do (i.e. more than nothing), but does not have a Ph. D..  I, on the other hand, do.  I would rather "degrade myself" by calling you the idiot/liar that you are, than be the idiot/liar who has been called out.

And I was trying to be civil all throughout. I like this place. It really tests my patience on civility.

Do you know what a module is? Don't answer that, if you knew what a module is, the case I was referring to should have been clear as day. But I'll humor the ignorance and illustrate the case.

Again: Idiot.

[liszt85]

I was hoping you would jump into the fray cause you've confessed to a phd degree in math.

Really? Could you please tell me where exactly I "confessed" to a PhD degree IN MATH??? So you're turning your focus elsewhere now that fft has exposed you? I suggest you move on.

[j_menz]

but does not have a Ph. D..  I, on the other hand, do. 

What in, may one ask, and from where?

[fftransform]

What in, may one ask, and from where?

In mathematics, from UAB, as of three weeks from now.  My research is in group theory, algebraic geometry, algebraic combinatorics and automorphic forms.

[jesc]

okay so maybe that phd was from another post.

Let's make this formal. Again.

Let R be a ring. Let A be an additive abelian group. Consider A as a (left) R-module
(ok, are we fine with this?)

3, 2 \in R and x \in A. Let R and A be disjoint, such that \forall r \in R, r\notin A and \forall a \in A a\notin R.

consider 3x + 2 again. You got that it isn't part of the module. That's exactly the case I wanted to show.

PhD and all, professionalism and all is it beyond all of you to make a formal criticism of the statements above?

I'm not angry. I'm not mad. I actually enjoy the emotional challenge of everyone bearing down on me on a forum. Anyone who takes an effort to properly criticize all of the above and I will certainly admit my mistakes and leave it at that.

[fftransform]

Let R be a ring. Let A be an additive abelian group.

There is not such thing as an "additive abelian group."  Every abelian group can be written additively.  That is how I will interpret your post from here on: $A$ is an arbitrary abelian group, written additively.

Consider A as a (left) R-module
(ok, are we fine with this?)

No.  If you proceed with this wording, you will get nowhere.  You mean, "let $R$ act on $A$ from the left."  $A$ is not the module.

3, 2 \in R and x \in A. Let R and A be disjoint, such that \forall r \in R, r\notin A and \forall a \in A a\notin R.

How a mathematician would write this: $2, 3 \in R, x \in A, R \cap A = \varnothing$.

consider 3x + 2 again.

I assume you mean in the module.  Ok, what about it?

$1 \notin R, \sigma(x) = 2; \forall r \in R, a \in A s.t. a \neq x, ra = 0.  3 \in R, 3x = 3x + 2; \forall r \in R s.t. r\neq 3, rx = 0, 3 + 2 = 3 \in R$.

There is a module where 3x + 2 is defined, despite your stipulations.  I made your ring $\mathbb{Z}_2$ and abuse your notation.  3x + 2 will, in general, not be defined in such a module; however, you made many other statements in your other post which were nonsense.  As well, again, nobody would bother mentioning a module.

[jesc]

There is not such thing as an "additive abelian group."  Every abelian group can be written additively.  That is how I will interpret your post from here on: $A$ is an arbitrary abelian group, written additively.


No.  If you proceed with this wording, you will get nowhere.  You mean, "let $R$ act on $A$ from the left."  $A$ is not the module.


How a mathematician would write this: $2, 3 \in R, x \in A, R \cap A = \varnothing$.


I assume you mean in the module.  Ok, what about it?

$1\notin R, \sigma(x) = 2; \forall r \in R, a \in A s.t. a \neq x, ra = 0.  3 \in R, 3x = 3x + 2; \forall r \in R s.t. r\neq 3, rx = 0$.

There is a module where 3x + 2 is defined, despite your stipulations.  

Finally a proper response I'm glad to read.

3x + 2 will, in general, not be defined in such a module

Exactly what I wanted to point out but you gave an example where 3x+2 is defined despite my stipulations. That's acceptable. If you did that from the get go then none of the previous altercations were necessary.

[fftransform]

Finally a proper response I'm glad to read.

I presented a case where 3x+2 isn't in the module but you gave an example where 3x+2 is defined despite my stipulations. That's acceptable. If you did that from the get go then none of the previous altercations were necessary.

You did not present such a case; you were not specific enough.  I can abuse your notation easily.  In general, 3x + 2 will not be defined in that module.  However, it was not the ultimate assertion that I objected to; you made many other statements in the post that I initially responded to.  Those are the statements which are bizarre.

Edit: btw, in your quote, which you apparently made between my edits, what is described is not actually a module.  I need 2 to be the additive identity of R, something I left off in the first version.

[jesc]

You did not present such a case; you were not specific enough.  I can abuse your notation easily.  In general, 3x + 2 will not be defined in that module.  However, it was not the ultimate assertion that I objected to; you made many other statements in the post that I initially responded to.  Those are the statements which are bizarre.

Edit: btw, in your quote, which you apparently made between my edits, what is described is not actually a module.  I need 2 to be the additive identity of R, something I left off in the first version.

The issue of 3x+2 not being defined was the only issue I'm concerned with since my second post on this thread. My only purpose was to outline that possibility. But that's already covered and both of us are repeating it over and over again.

[liszt85]

fft, jesc is actually your adviser. He/she just wanted to test you one final time. You will get your degree tomorrow in the mail, you won't have to wait 3 weeks. Good luck.

PS: I wish I had taken group theory as an undergrad. It sounds like a lot of fun.

[fftransform]

PS: I wish I had taken group theory as an undergrad. It sounds like a lot of fun.

Basic group theory is moderately self-teachable, although you may get hung up on a couple of things, as nearly all students do (specifically quotient groups, Sylow's Theorems, normal series, central series, the Frattini subgroup and commutator subgroups).  Group theory can be studied to an extremely high level in a pretty self-contained manner (even up into current research areas), without venturing out into other areas of upper level mathematics.  As of right now, the main areas of research in group theory are:

Thin groups, which only requires a basic knowledge of graph theory,
discrete groups and abstract harmonic analysis (via automorphic forms: not approachable),
lie representations (approachable if you're willing to beef up on linear + multilinear algebra),
p-adic representations (not approachable; requires a lot of number theory),
classical invariant theory (not approachable: requires a lot of combinatorics),
and fusion systems (self-contained, but very high level).

Computational group theory using GAP (a computer program) is also popular atm, but what exactly they're doing I'm not sure.  It's not relevant to automorphic forms or fusion systems, which is what I study in the context of group theory.  For the most part, they're just compiling absolutely as much info as possible on groups of small and medium order (say, under 1000 elements).

I can send you a PDF of Dummit-Foote, the standard intro text, if you think you're interested.

[ahinton]

In mathematics, from UAB, as of three weeks from now.  My research is in group theory, algebraic geometry, algebraic combinatorics and automorphic forms.

As a matter of interest, could you point me in the direction of your PhD dissertation when it becomes available? Not for me, mind! - by saying which I do not wish to appear rude - I mean that I openly admit that its contents would be well above my head - but because I know two mathematicians who happen also to be heavily involved in the Sorabji cause and I'm sure that it would be of interest to them (there would have been a third but, sadly, Charles Hopkins died, as you probably know, just over 5 years ago at the age of 55). If you prefer to send details of this privately, then by all means do so to my email address which I'm sure you have.

Thanks in advance.

Best,

Alistair

[liszt85]

Basic group theory is moderately self-teachable, although you may get hung up on a couple of things, as nearly all students do (specifically quotient groups, Sylow's Theorems, normal series, central series, the Frattini subgroup and commutator subgroups).  Group theory can be studied to an extremely high level in a pretty self-contained manner (even up into current research areas), without venturing out into other areas of upper level mathematics.  As of right now, the main areas of research in group theory are:

Thin groups, which only requires a basic knowledge of graph theory,
discrete groups and abstract harmonic analysis (via automorphic forms: not approachable),
lie representations (approachable if you're willing to beef up on linear + multilinear algebra),
p-adic representations (not approachable; requires a lot of number theory),
classical invariant theory (not approachable: requires a lot of combinatorics),
and fusion systems (self-contained, but very high level).

Computational group theory using GAP (a computer program) is also popular atm, but what exactly they're doing I'm not sure.  It's not relevant to automorphic forms or fusion systems, which is what I study in the context of group theory.  For the most part, they're just compiling absolutely as much info as possible on groups of small and medium order (say, under 1000 elements).

I can send you a PDF of Dummit-Foote, the standard intro text, if you think you're interested.

Please send me the pdf! I'd love to take a look. My email id is impromptu.pianist AT gmail.com
Thanks.

[fftransform]

Please send me the pdf! I'd love to take a look. My email id is impromptu.pianist AT gmail.com
Thanks.

Ok, attaching.  You'll have it in just a bit.  In the mean time, please download a .djvu viewer; I used .djvu rather than PDF, because it is more compact and the book is ~950 pages.