47,570 reputation
842112
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location USA
age
visits member for 2 years, 6 months
seen 2 hours ago

PhD

Interests:

Ring and module theory

Clifford algebra/Geometric algebra

Mathematical physics

Applications of abstract algebra


2h
comment Is the ring of entire functions coherent?
@GeorgesElencwajg : I knew the single variable case was Prufer, but I don't know anything about the multivariable case. Alas since it's not the case we can't use the semihereditary $\implies$ coherent implication...
3h
comment Is the ring of entire functions coherent?
@GeorgesElencwajg Because an affirmative answer gives a simple solution to the problem at hand. I don't think it's worth starting a whole new question for something I am not really interested in and then coming back here and pointing to the answer.
4h
answered Semisimple modules and the radical
6h
comment Is the ring of entire functions coherent?
Do you happen to know offhand if the ring you're talking about is a Prufer domain? Or a Bezout domain?
6h
comment Is the ring of entire functions coherent?
@user26857 I guess so! I actually didn't look at the wiki and was just working from memory with the "products of flats are flat" definition. Next question: is this ring of entire functions a Prufer domain?
8h
revised What is the relationship between parallelogram law and polarisation identity?
langle/rangle
8h
comment Quaternion - Spinor relationship?
@Neal OK: I know what you mean then. Thanks for the comment.
8h
comment Is the ring of entire functions coherent?
Dear @GeorgesElencwajg: Do you happen to know if what the OP is describing the same thing as a coherent ring?
9h
revised Quaternion - Spinor relationship?
edited tags
9h
comment Quaternion - Spinor relationship?
Dear Neal: Quick question: Of course there are many important topological projective spaces, but I'm wondering about the phrase "topologically a projective space." It seems to suggest that the projectiveness of the space is characterized by its topology, which I don't think is what you meant. Or is there actually a way to characterize topological spaces as projective based on their topology? Regards
9h
comment Quaternion - Spinor relationship?
@JCW There are no doubt hundreds of web pages explaining the connection, but I know that many of them are written by physicists, and hence long, involved and example-centric. I bet there's a terse algebraic bundling, but unfortunately I haven't internalized spinors enough yet to say what it is. I used to think they were related to simple modules of Clifford algebras, but I never learned the details well.
9h
comment Quaternion - Spinor relationship?
@JCW Actually I had meant to include the link that led me to that page too. I added it also.
9h
revised Quaternion - Spinor relationship?
added 207 characters in body
10h
answered Quaternion - Spinor relationship?
10h
answered Equivalent definitions of an algebra over a ring
20h
comment Prove the set, {y ∈ X | r ≤ d(x,y) ≤ s}, is closed
Do you believe in closed balls and open balls? You could make it the intersection of a closed ball with the complement of an open ball: a closed set.
1d
comment prove that if $\exists a\in A\space:\space stb(a)\not=\{e\}$ then the action is unfaithful
@AmitaiYuval OK: replacing $A$ with a singleton is simpler, but much simpler might be an overstatement :)
1d
revised A counterexample to $Ae\simeq Ae^{\prime}\to A(1-e)\simeq A(1-e^{\prime})$
edited tags
1d
revised A counterexample to $Ae\simeq Ae^{\prime}\to A(1-e)\simeq A(1-e^{\prime})$
deleted 18 characters in body
1d
comment Krull-Schmidt theorem and internally cancellable modules?
Thanks for reopening it. Glancing at the link, I think the example I'm giving is different from the ones given there.