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 Dec 15 revised Surjective homomorphism in Laurent polynomial ring. added 15 characters in body Dec 15 asked Surjective homomorphism in Laurent polynomial ring. Dec 14 comment Sum involving units of a ring. You are right, I didn't realize this solution... However, what happens if we assume that $A$ is a discrete valuation ring? Dec 14 comment Sum involving units of a ring. @Joel Cohen: You are right, I didn't realize this solution... However, what happens if we assume that $A$ is a discrete valuation ring? Dec 14 revised Sum involving units of a ring. edited body Dec 14 asked Sum involving units of a ring. Nov 27 comment Binomials in associative algebras Ok, I got it... Thanks! Now I see why you mentioned combinatorial Nullstellensatz. When I read your proof at the first time, I was confused in what you took as the domain. Thanks again! Nov 26 awarded Commentator Nov 26 comment Binomials in associative algebras I still don't understand how you pass to $A$ from the situation with nonnegative integers. I understand the idea and the fact that $P(k_1,k_2)=0$ for all $k_1,k_2\in \mathbb Z_+$. But after you write "In other words" I am confused... Nov 26 accepted Binomials in associative algebras Nov 26 comment Binomials in associative algebras @Qiaochu Yuan: THANKS. I will appreciate too much. Nov 26 comment Binomials in associative algebras @QiaochuYuan: I don't see how to proceed by induction in this case. In the case of natural numbers we have to divide by expressions involving $x$ and $y$ at some point. But here we can't... So, what is the procedure to show the formula above? Nov 26 comment Binomials in associative algebras @Qiaochu Yuan: So, are you saying that it holds with the assumption that $A$ is an associative and commutative $Q$-algebra? Nov 26 awarded Peer Pressure Nov 26 awarded Scholar Nov 25 asked Binomials in associative algebras Jun 28 awarded Self-Learner Feb 18 comment Eigenspaces of a representation Let $\rho: g \mapsto gl(V)$ such representation. The generalized eigenspace of $V$ via $\rho$ is $$V_i=\left\{v\in V \mid \forall x\in g, \exists n\in \mathbb N \text{ such that } (\rho(X) - \lambda_i(X))^nv = 0\right\}.$$ Feb 18 revised Eigenspaces of a representation added 7 characters in body Feb 18 asked Eigenspaces of a representation