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Feb
8
revised Is it accurate to say that multiplication of two integers yields an integer?
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Feb
8
comment Is it accurate to say that multiplication of two integers yields an integer?
@graydad oh, gotcha
Feb
8
answered Is it accurate to say that multiplication of two integers yields an integer?
Feb
8
comment Prove that if $X$ and it's closure $\overline X$ are connected and if $X\subset Y \subset \overline X$, show that Y is also connected.
@EmotionallyVulnerableLlama I think if you stop and think carefully about how this proof works, you'll realize you are distracting yourself. I am showing that all disconnections of Y are trivial. That is, if Y is contained in the union of two open sets whose intersection in Y is empty, then one of them already contains Y. A nontrivial disconnect would be a pair of such sets which both contain points of Y.
Feb
8
comment Prove that if $X$ and it's closure $\overline X$ are connected and if $X\subset Y \subset \overline X$, show that Y is also connected.
@EmotionallyVulnerableLlama the conclusion is that $Y$ cannot be disconnected with open sets (there is no contradiction because it is not a proof by contradiction) So, Y is connected
Feb
7
comment When is an ideal also a ring, and could then be anything said about its relation to the original ring
@Stefan $e$ is in the ideal $eR$, so it absorbs (1-e)R$ into $eR$ as well. Without $eR(1-e)=0$, $e$ would not be a right identity
Feb
7
comment How to wite a Statement of Purpose for a Summer Program in Representation Theory.
Whatever you write, spellcheck it better than you did on this post.
Feb
7
revised When is an ideal also a ring, and could then be anything said about its relation to the original ring
added 218 characters in body
Feb
7
comment Monoids and groups
that does not appear in the expression $s_1s_2s_1^{-1}s_2^{-1}$
Feb
7
comment Monoids and groups
There is at least one problem with what you've written: for example, why should $s_1^{-1}s_2^{-1}$ be the inverse of $s_1s_2$? After overcoming that, you could probably be a bit more thorough about your conclusion
Feb
6
answered When is an ideal also a ring, and could then be anything said about its relation to the original ring
Feb
6
comment When is an ideal also a ring, and could then be anything said about its relation to the original ring
@Stefan yes, there are, and the description you provided for "subring" is a little ambiguous. In the very first description It would be best to emphasize that the $1$ in both rings is the same element (since $1$ can be interpreted as generic notation for the identity of whatever ring is currently being talked about.) this makes the distinction from your later line of thought clear.
Feb
6
comment Show that all simple modules of ${M_n}{(D)}$ are isomorphic to $D^n$, where $D$ is a division ring.
The solutions I linked to do prove c) from b), and you're right that not all minimal ideals are in the collection of $C_l$, but that is irrelevant. I just meant to point out how one minimal right ideal is isomorphic to $D^n$ and then the solutions demonstrate there can't be other types.
Feb
6
comment Embeddable rings axiomatic class?
@NoahSchweber you can find an example of a domain which does not embed in any division ring appears in Lectures on modules and rings by Lam in the chapter on noncommutative localization
Feb
6
comment Embeddable rings axiomatic class?
The bit about noncommutativity isn't necessary then, since subrings of fields are all commutative.
Feb
5
comment Why are math textbooks that are considered good books so hard to read? Why do authors make their books difficult to read?
@fleablood Case in (your) point, I can think of a lot of explanations written by physicists of certain mathematics that seemed positively impenetrable. I guess the extra talk was meant to be expository, but it was usually more of a hindrance than help in the cases I'm thinking of.
Feb
5
comment A method of writing all primes
This can be explored programmatically to a great extent, but the combinatorics blow up very early on. Guess it doesn't bother you that $2,3$ don't fit, either.
Feb
5
revised A method of writing all primes
spelling, whitespace
Feb
5
comment Show that the left ideal $(N_G) \subset F[G]$ is a simple submodule of $F[G]$, where $N_G = {\sum}_{g \in G} {g} \in F[G]$.
Please try out the site's search function first, next time. I think you would have found the linked duplicate.
Feb
5
answered Show that the left ideal $(N_G) \subset F[G]$ is a simple submodule of $F[G]$, where $N_G = {\sum}_{g \in G} {g} \in F[G]$.