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Feb
5
comment Show that all simple modules of ${M_n}{(D)}$ are isomorphic to $D^n$, where $D$ is a division ring.
Obviously any of the $C_l$ are isomorphic to $D^n$.
Feb
5
comment Show that all simple modules of ${M_n}{(D)}$ are isomorphic to $D^n$, where $D$ is a division ring.
Strategy in a nutshell: every simple right module embeds as a minimal right ideal, and then the product of two nonisomorphic minimal right ideals has to be zero. This cannot occur in a simple ring, since if $B\neq \{0\}$, $AB=\{0\}$ implies that $A=\{0\}$.
Feb
5
comment Show that all simple modules of ${M_n}{(D)}$ are isomorphic to $D^n$, where $D$ is a division ring.
Please make use of the search feature and the related questions that pop up while you ask a question. math.stackexchange.com/a/874720/29335 and math.stackexchange.com/q/1060896/29335 will also be helpful (they are related to the dupe.)
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?
Dear al jebr :Flame-bait rants are off topic. Please take it to your blog, regards.
Feb
4
answered Is the following set a group?
Feb
4
comment Geometry perpendicular proof
Given what axioms?
Feb
4
comment why is the collection of all finite subsets of $\mathbb{R}$ not a $\sigma-ring$
@josh Of course any finite ring in this definition would automatically be a $\sigma$ ring, since every countable union would actually boil down to a finite one. But as for your $A$ and $B$ example, do you mean that you want $B=A^c$?
Feb
4
comment Size of a point.
@SeñorPérez No problem. See you around
Feb
4
revised Relationship between operations of a ring
added 108 characters in body
Feb
4
answered Relationship between operations of a ring
Feb
4
revised Size of a point.
added 4 characters in body
Feb
4
answered Size of a point.
Feb
4
comment Complex numbers as linear operators?
Well, not all functions on $\Bbb R^2$ are linear operators, but yes, dilation/rotations are linear operators.
Feb
3
comment The coordinate ring of $\varepsilon: xy-1=0$
and also math.stackexchange.com/q/1415542/29335
Feb
2
comment Principal ideal domain with finitely many ideals
Here's the same problem rephrased for UFDs. Maybe not a dupe, but definitely a generalized-dupe.
Feb
2
comment Principal Ideal Domain $R$ and ideal $J\neq 0$ so that that $R/J$ have a finite number of ideals.
Never mind, found a closer duplicate with an answer. Please use the search feature next time.
Feb
2
comment Principal Ideal Domain $R$ and ideal $J\neq 0$ so that that $R/J$ have a finite number of ideals.
No effort duplicate of math.stackexchange.com/q/640403/29335. Unfortunately, those helping that poster only made comments and no solutions. I left a CW answer to rectify the situation. If someone upvotes that then this can be closed as a dupe of that one.
Feb
2
answered Unique factorization domain and principal ideals .
Feb
2
comment Are “$S$-monoids” known to be good for anything?
Hm, what a strange choice to call the set which is acting by the set it is acting upon. It clashes with established terminology like this: $X$ is a $G$-set if it has some action $G\times X\to X$. A more likely name would be something like "$S$ is an (adjective) $M$-monoid." But anyhow, may I ask how you came upon the construction? Just through the context of the 'main example'?
Feb
2
comment Which of the following are true about the ring of continuous real valued functions C[0,1]
d) is false for all sorts of reasons. You should be able to come up with some thoughts on that one.