In this paper, we establish the analogue of some recent lineability and algebrability results on the sets of sequences and series within the context of p-adic analysis. More specifically, we prove (among several other results) that: (i) in the space of all p-adic sequences, the set of all convergent sequences for which Cesaro’s Theorem fails is lineable, (ii) the set of all non-absolutely convergent p-adic series considered with Cauchy product or pointwise product is algebrable in $$c_0$$ .

中文翻译：

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非阿基米德设置中的代数通用性和可和性

在本文中，我们在 p-adic 分析的上下文中建立了一些最近的线性和代数结果对序列和序列集的模拟。更具体地说，我们证明（在其他几个结果中）：（i）在所有 p-adic 序列的空间中，Cesaro 定理失败的所有收敛序列的集合是可线性的，（ii）所有非绝对序列的集合使用柯西积或逐点积考虑的收敛 p-adic 系列在 $$c_0$$ 中是可代数的。