Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2021 / Cilt: 70 - Sayı: 2

A variant of the proof of Van der Waerden's theorem by Furstenberg

Sadık EYİDOĞAN, Ali Arslan ÖZKURT

Sayfa
1065–1072
DOI
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Abstract

Let RR be a commutative ring with identity. In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of RR, we will define a metric on RR using them. Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].