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Tagged with laurent-polynomials polynomials
4 questions
9
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1
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687
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Number of Laurent monomials of n variables with degree at most d
Introduction: We have a question of how to calculate the number of $n$-variables Laurent monomials of degree at most $d$.
For example: If $n=2$, $d=2$ then we have 19 monomials, which are:
$x^{-2}$, $...
1
vote
1
answer
387
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Automorphisms of the ring of Laurent polynomials
Is the group of automorphisms of the ring $\mathbb{F}[t,t^{-1}]$ of Laurent polynomials known? Here, $\mathbb{F}$ is an algebraically closed field of characteristic $0$ and I am considering not ...
7
votes
2
answers
366
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Idempotent Laurent polynomials (in noncommuting variables)
Let $K$ be a field and $R=K\langle X_1,\dots,X_n,X_1^{-1},\dots,X_n^{-1}\rangle$ the Laurent polynomial ring in $n$ noncommuting variables. Can $R$ have idempotents distinct from $0$ and $1$?
4
votes
1
answer
434
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Cancellation problem for Laurent polynomial rings and power series rings
Throughout, let $k$ be an algebraically closed field. For two $k$-algebras $A,B$ let us write $A \cong_k B$ to mean that $A,B$ are isomorphic as $k$-algebras.
It is known that if $A$ is an integral ...