幂等元附近某些大集的乘积

Product of some large sets near idempotent

Surajit Biswas, Sourav Kanti Patra, Sabyasachi Dey

备注：: The authors, paper title, and content have been updated in the published version

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AI总结：

本文研究幂等元附近中心集等大集的有限与无限笛卡尔积性质、张量积影响及集合丰富性，并将 Milliken-Taylor 定理多项式推广至零附近。

摘要：

我们刻画了幂等元附近中心集的有限笛卡尔积何时在幂等元附近仍是中心集。此外，我们对其无限笛卡尔积给出了部分刻画。随后，我们研究了幂等元附近某些大集的丰富性，并考察了幂等元附近张量积的作用。最后，作为应用，我们给出了零附近 Milliken-Taylor 定理的多项式推广。

英文摘要：

We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover, we provide a partial characterization for the infinite Cartesian product of the same. Then, we study the abundance of some large sets near idempotent. Also, we investigate the effect of tensor product near idempotent. Finally, as an application we provide the polynomial extension of Milliken-Taylor theorem near zero.

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