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73294
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location USA
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visits member for 2 years
seen 5 hours ago

PhD

Interests:

Ring and module theory

Clifford algebra/Geometric algebra

Mathematical physics

Applications of abstract algebra


1d
revised Prove $M$ is a Maximal Ideal in $\Bbb Z\times \Bbb Z$
tex
1d
answered Prove $M$ is a Maximal Ideal in $\Bbb Z\times \Bbb Z$
1d
revised Characteristic of Integral-domain where $15a=0$ but $3b\neq 0$.
text markup, better title
1d
answered Epimorphism affect on Ideals
1d
answered valuation ring is a field?
1d
comment Show that a particular set is a poset
I went ahead and made the title lowercase, and I also added tags beyond "homework". Homework tag is not supposed to be used alone.
1d
revised Show that a particular set is a poset
edited tags
2d
comment What is the reason for stating Cayley's theorem this way?
@anaconda if you view this as a structure theorem, then yeah, it is tempting to say the theorem is sharpened by using G and not X. But actually it isn't much of a structure theorem, it's more of a representation theorem.
2d
revised What is the reason for stating Cayley's theorem this way?
added 12 characters in body
2d
revised What is the reason for stating Cayley's theorem this way?
added 12 characters in body
2d
comment What is the reason for stating Cayley's theorem this way?
@Seth Using the first statement, one can show that the class of such representations is exactly the class of functors of the category G into the category of sets. It's nice to know both versions, though, really.
2d
answered What is the reason for stating Cayley's theorem this way?
2d
comment Every radical is prime?
It is true that every radical is semiprime, that is, an intersection of prime ideals.
2d
answered divisible modules
2d
comment Necessary and sufficient condition for $r(\mathfrak a)$ to be prime
@amateur I added material for that question.
2d
revised Necessary and sufficient condition for $r(\mathfrak a)$ to be prime
added 385 characters in body
2d
comment What is the difference between a module of finite rank and finitely generated module.
@user2902293 That's a good example in commutative rings, yes.
2d
comment what does this triangle-like notation mean?
Fortunately in this case the context is narrow enough to take a guess. In general though, if you have a question about notation, give a line or two of context where it is used. After all, not all mathematical symbols have a fixed universal meaning in all contexts.
2d
comment Why is the cross product contained in orthogonal complement?
@sj134 Hm, yes, but I was asking if you know why that is true. Just let me know if I can help with anything else.
2d
comment Where am I going wrong with this limit?
@user127700 Please include the L'Hopital's method you tried so we can inspect it for the problem.