Bohl代数的Bass稳定秩和拓扑稳定秩都是无限的
The Bass and topological stable ranks of the Bohl algebra are infinite
摘要:
玻尔代数$\textrm{B}$是函数$t^k e^{λt}$的线性组合的环,其中$k$是任何非负整数,$λ$是任何复数,具有逐点运算。我们证明了$\textrm{B}$的Bass稳定秩和拓扑稳定秩(其中我们使用一致收敛拓扑)是无限的。
英文摘要:
The Bohl algebra $\textrm{B}$ is the ring of linear combinations of functions $t^k e^{λt}$, where $k$ is any nonnegative integer, and $λ$ is any complex number, with pointwise operations. We show that the Bass stable rank and the topological stable rank of $\textrm{B}$ (where we use the topology of uniform convergence) are infinite.
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