Product of some large sets near idempotent

TL;DR

This paper explores the properties of large sets near idempotent elements, characterizing their behavior under finite and infinite Cartesian products, tensor products, and extending classical theorems in this context.

Contribution

It provides new characterizations of central sets near idempotent under Cartesian products and extends the Milliken-Taylor theorem near zero.

Findings

Finite Cartesian product of central sets near idempotent remains central near idempotent.

Partial characterization for infinite Cartesian products of such sets.

Polynomial extension of Milliken-Taylor theorem near zero.

Abstract

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.