论文标题
有关线性复发序列的一些代数结果
Some algebraic results concerning linear recurrence sequences
论文作者
论文摘要
我们研究了所有$ f $ - vector-vector Spaces $ l（p）$的集合$ \ MATHCAL {l} _ {f} $，其中$ p $是monic的，而$ f $和$ l（q）$分配了$ f $ the Linlinear Recurrence sequences to $ f $，带有特色polynomial $ q $。我们表明，$ \ Mathcal {l} _ {f} $可以赋予两个分级的通勤半级结构。这项研究使我们能够以紧凑的形式获得多项式$ p，q \ in f [x] $中的$ l（p）= \ prod_ {i = 1}^{m} l（p_ {i}）$ and $ l（q）= l（p_ {1}）= l（p_ {1}） \ ldots，p_ {m} $是$ f $的任何一元多项式。
We study the set $\mathcal{L}_{F}$ of all $F$-vector spaces $L(P)$ where $P$ is monic and splits over $F$ and $L(Q)$ denotes the set of linear recurrence sequences over $F$ with characteristic polynomial $Q$. We show that $\mathcal{L}_{F}$ can be endowed with two structures of graded commutative semiring. This study allows us to obtain, in compact forms, the polynomial $P,Q\in F[X]$ such that $L(P)=\prod_{i=1}^{m}L(P_{i})$ and $L(Q)=L(P_{1})\ast\cdots\ast L(P_{m})$, where $P_{1}, \ldots, P_{m}$ are any monic polynomials over $F$.
