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arXiv · 2407.10576

Vector spaces over finite commutative rings

Jun Guo·Junli Liu·Qiuli Xu
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Abstract

Vector spaces over finite fields and Anzahl formulas of subspaces were studied by Wan (Geometry of Classical Groups over Finite Fields, Science Press, 2002). As a generalization, we study vector spaces and singular linear spaces over commutative rings, and obtain some Anzahl formulas and dimensional formula for subspaces. Moreover, we discuss arcs and caps by using these subspaces.

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Jun Guo, Junli Liu, Qiuli Xu. 2025-03-27. Vector spaces over finite commutative rings. https://arxiv.org/abs/2407.10576

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