Sperner’s theorem for non-free modules over finite chain rings

The article delves into the application of Sperner's theorem to non-free modules over finite chain rings, a significant extension of classical results. It explores the properties of these modules, including their poset structures and the behavior of antichains. The research presents new theorems and techniques, providing a deeper understanding of the Sperner property in these contexts. The paper is organized into sections that cover preliminary results, specific cases for chain rings of different lengths, and generalizations of known theorems. The findings offer valuable contributions to the field of combinatorics and algebra, making this article a must-read for specialists in these areas.