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2m
comment A concrete example of a unital noncommutative ring without maximal two-sided ideals
The problem when you do not have a $1$ is that une union of a totally ordered set of proper ideals need not be a proper ideal.
3m
answered A concrete example of a unital noncommutative ring without maximal two-sided ideals
1h
revised Commutative Diagrams and Polynomials
edited tags
1h
answered Commutative Diagrams and Polynomials
4h
comment Fixed field of the subgroup of $Aut_{K}{K(x)}$
No one writes $1_K$...
2d
comment Is this simple drawing a category?
Yes. ${}{}{}{}{}$
2d
comment Local ring and zero divisors
@NECing, in what possible way this does not answer the question?!
2d
comment Diagrams characterizing ring characteristic, and in particular field characteristic 1?
Moreover, the field with one element is not a field (and it may not be at all, for all we know...)
2d
comment Diagrams characterizing ring characteristic, and in particular field characteristic 1?
I don't understand what you want.
2d
answered Is there a classification for the generating sets of symmetric group?
2d
answered Is this ring a well known ring and if so how is it called?
Oct
21
comment Exterior derivative of local basis element $dx^k$ is zero
You should give us what definition you are using of $dx^k$ and of the exterior differential, as the details of the proof depend on them.
Oct
19
comment space of solutions of a PDE
On the other hand: the statement of the problem makes no implication that one can deduce that the set of solutions for a fixed K is a vector space from the fact that there is «a fixed amount of solutions». As I said, the two things are completely independent.
Oct
19
comment space of solutions of a PDE
The set of solutions of a linear homogeneous PDE is always a vector space: that is, in fact, almost what it means for the equation to be linear and homogeneous!
Oct
19
comment space of solutions of a PDE
The fact that the set of solutions of the equation (for a fixed K) is a vector space is just a fact of nature, a consequence of the equation being linear homogeneous).
Oct
19
comment space of solutions of a PDE
I don't understand what you don't understand: what is to «link the two solutions in to a the equation being a vector space»? I don't see what two things you are trying to connect.
Oct
19
comment space of solutions of a PDE
If they are not the same function then you have two solutions.
Oct
19
comment space of solutions of a PDE
Well, are $\sin\pi x\sin\pi 2y$ and $\sin2\pi x\sin\pi y$ the same function? In any case, by «number of solutions» they probably mean number of «linearly independent solutions».
Oct
16
comment Questions related to the concept of $k$-algebras
In fact, what you describe as a motivation for studying algebras is not a motivation at all.
Oct
16
answered Questions related to the concept of $k$-algebras