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Jan
12
comment Is $\operatorname{End}(V)\simeq M_n(D)$?
Well, actually. Come to think of it. It probably goes like $\operatorname{End} R^n \cong M_n (R^\mathrm{op})$. Doesn’t matter much, though, because the opposite ring of a division ring is again a division ring and the definition of prime rings seems to be symmetric.
Jan
12
comment Is $\operatorname{End}(V)\simeq M_n(D)$?
Ah, so your question is only about $\operatorname{End} D^n \cong M_n(D)$? You can write down the isomorphism known from linear algebra. It works. (If you don’t know it, guess it, check it. It works.)
Jan
12
comment Is $\operatorname{End}(V)\simeq M_n(D)$?
So what does a mean for a vector space to be $n$-dimensional?
Jan
10
accepted Is there a name for a monoid with a distinguished absorbing element?
Jan
2
comment General definition of free module over arbitrary rings and space of multi-linear functions
You have to clean up this question a bit.
Dec
23
comment If $(-1) \cdot (-1) = +1$ shouldn't $(+1) \cdot (+1) = -1$?
Is this voted down because the proposal is unreasonable? Is that a reason to vote down? Or is this maybe considered a troll question?
Dec
18
revised If $u$ is a unit in $S$, then $u$ is a unit in $R$
deleted 2 characters in body
Dec
18
comment If $u$ is a unit in $S$, then $u$ is a unit in $R$
Just simply use $S ⊂ R$. If for some $u ∈ S$ there is some $v ∈ S$ with $uv = 1$, then – as $S ⊂ R$ – both $u$ and $v$ are also in $R$.
Dec
18
answered If $u$ is a unit in $S$, then $u$ is a unit in $R$
Dec
18
comment How to explain that null $A$=(row$A$)$^\perp$?
That doesn’t give you a description of the kernel of $A$ now, does it? Could be anything of the correct dimension, right?
Dec
14
comment Calculate $\:\lim_\limits{ \Large_{z \to c}}\:\:{\frac{z^n - c^n}{z-c}} ~~ c,z \in \mathbb{C}\:$ without L'Hopital's rule
I edited your question: I corrected the problem statement and deleted your edit where you corrected it (as is customary for corrections on this site). I also erased the <br> tags before and after the math formula, for they are not needed there, and I deleted the “thanks” (as is customary for this site). Hope that’s okay.
Dec
14
revised Calculate $\:\lim_\limits{ \Large_{z \to c}}\:\:{\frac{z^n - c^n}{z-c}} ~~ c,z \in \mathbb{C}\:$ without L'Hopital's rule
corrected the problem statement according to the edit
Dec
14
comment Find a family of open sets whose intersection is compact.
Or even $∅$, right?
Dec
14
comment Find a family of open sets whose intersection is compact.
Well, actually, $­­­­­∅$ is compact as well, …
Dec
14
comment Find a family of open sets whose intersection is compact.
It is (if you use $3-1/n$ in the lower bound instead of $3+1/n$). But you can even find a more minimal example (exploiting the same idea).
Dec
14
comment Are Standalone Introductory Linear Algebra Classes Bad?
I don’t think this question is off-topic, but it’s definitely a soft-question, so you should use this tag. Regarding the question, maybe the author just means that a whole course on linear algebra might be unnecessarily much for a introductory course to differential equations? I can’t see why it might be bad – it surely helped me a lot with studying the basics of (linear) differental equations.
Dec
12
accepted What does the theory of the empty set look like?
Dec
12
comment What does the theory of the empty set look like?
This is actually where the question came from – a friend and I realised that the inference rules for first order logic are inconsistent with the empty set and we were wondering if the theory of the empty set is truly an extension of first order logic. Only after asking the question we realised that the inference do preassume nonempty models. Gonna accept this one now.
Dec
11
revised What does the theory of the empty set look like?
added 143 characters in body
Dec
11
comment What does the theory of the empty set look like?
1. Did you mean to say “$∀x∀y(x = y)$? 2. If so, if the model contains exactly one element “$∀y∀x(x = y)$” should be true as well. 3. Else, “$∀x (x = x)$” should be the axiom of reflexivity, no?