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9 votes
1 answer
687 views

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: $x^{-2}$, $...
Thien's user avatar
  • 93
1 vote
1 answer
387 views

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 ...
cl4y70n____'s user avatar
7 votes
2 answers
366 views

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 $1$?
Ralle's user avatar
  • 491
4 votes
1 answer
434 views

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 ...
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