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Apr
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Feb
19
comment Problem 1.24, Introduction to representation theory, Etingof
My first comment contains a typo which is clarified in my second comment. Regular representation means $A\oplus A$ acts on itself by multiplication. $(1,1)$ is a cyclic vector obviously. Subrepresentations include $A\oplus 0$ and $0\oplus A$. As for the downvote, you'll need to ask whoever did it.
Jan
30
comment Definitions of valuations in terms of totally ordered group
Thank you! What are some of the 'mild hypotheses' referred to in para 2?
Jan
30
accepted Definitions of valuations in terms of totally ordered group
Jan
30
asked Definitions of valuations in terms of totally ordered group
Nov
19
revised Problem 1.25 of Etingof: Indecomposable rep which is not cyclic
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Nov
18
comment Problem 1.25 of Etingof: Indecomposable rep which is not cyclic
I see what you mean now, and you're right. My apologies.
Nov
18
revised Problem 1.25 of Etingof: Indecomposable rep which is not cyclic
added 2 characters in body
Nov
18
revised Problem 1.25 of Etingof: Indecomposable rep which is not cyclic
added 2 characters in body
Nov
18
revised Problem 1.25 of Etingof: Indecomposable rep which is not cyclic
added 242 characters in body
Nov
3
asked Problem 1.25 of Etingof: Indecomposable rep which is not cyclic
Oct
28
asked Prime ideals in non-commutative ring
Oct
27
comment Problem 1.24, Introduction to representation theory, Etingof
I mean the regular representation of $A\oplus A$
Oct
27
comment Problem 1.24, Introduction to representation theory, Etingof
The representation $A \oplus A$ of $A$ has cyclic vector $(1,1)$ but is decomposable...
Oct
21
comment Why is axiom of choice needed? (Equivalent conditions for Noetherian)
I think I see what it is now. It is not induction at all as I'm not proving statements... I'm just abusing the term 'doing things by induction', meaning I can't actually write down the 'statement to prove' in the n-th step in first order or whatever unless (n-1)th step (ie picking the submodule) has already been done. Am I right?
Oct
19
comment Can the induced function of non-zero $f \in R[X]$ be zero, when $R$ is an infinite non-integral domain?
$R = \mathbb{Z}_4^{\mathbb{N}}$ with $f(X) = 2X(X-1)$ by the same token. I was clearly overthinking...
Oct
19
accepted Can the induced function of non-zero $f \in R[X]$ be zero, when $R$ is an infinite non-integral domain?
Oct
19
revised Can the induced function of non-zero $f \in R[X]$ be zero, when $R$ is an infinite non-integral domain?
added 242 characters in body
Oct
19
asked Can the induced function of non-zero $f \in R[X]$ be zero, when $R$ is an infinite non-integral domain?
Oct
19
revised What is a quick proof that $f \in \mathbb{C}[X_1,\dotsc,X_n]$ is determined by its induced function on $\mathbb{C}^n$?
added 130 characters in body; edited tags