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Factoring formal power series over principal ideal domains
power series principal ideal domains Commutative Algebra
2011/9/20
Abstract: We provide an irreducibility test and factoring algorithm (with some qualificiations) for formal power series in the unique factorization domain $R[[X]]$, where $R$ is any principal ideal do...
Optimal Tracking Control Design of Quantum Systems via Tensor Formal Power Series Method
Optimal Tracking Hamilton-Jacobi equation Quantum Systems
2009/9/25
In this study, in order to generate a sequence of desired quantum states (or quantum bits) for quantum communication and computation, it is more appealing to formulate a quantum control system as a bi...
A GENERALIZED CHAIN RULE FOR FORMAL POWER SERIES
Formal power series composition chain rule right distributive law
2008/11/25
Given a formal power series g(x) = P1n=0 bn xn and a nonunit f(x) = P1 n=1 an xn,
it is well-known that the derivative of the composition of formal power series satisfies the
Chain Rule, that is, (g...
Rickart-type Annihilator Conditions on Formal Power Series
Annihilator conditions Nearrings Skew power series Baer rings a-rigid rings Rickart rings
2010/2/25
Let R be an a-rigid ring and R0[[x;a]] be the nearring of a formal skew power series in which addition and substitution are used as operations. It is shown that R is Rickart and any countable family o...
Two Lemmas on Formal Power Series
Formal power series Local fields Formal groups Lubin-Tate theory Coleman power series
2010/3/3
Let L be a local field and \tilde{L} the completion of the maximal unramified extension of L. In this short note, we prove \noindent (I) the sequences \noindent (1\prime\prime) 0\rightarrow {\cal O}L...