论文标题

50年有限的几何形状,“有限环的几何形状”部分

50 years of Finite Geometry, the "geometries over finite rings" part

论文作者

Keppens, Dirk

论文摘要

尽管对于一个很大的部分,在过去的50年中,有限的几何形状集中在有限场上的几何形状上,而不是分区环的有限环上的几何形状受到了较少的关注。然而,几个重要的有限环产生了有趣的几何形状。在本文中,我们汇总了一些散布在文献上的结果,这些结果涉及有限的环和这种环上的平面投射几何形状。它不包含新材料,但是通过在一个地方收集东西,我们希望在至少50年的有限几何形状中刺激该领域的进一步研究。

Whereas for a substantial part, Finite Geometry during the past 50 years has focussed on geometries over finite fields, geometries over finite rings that are not division rings have got less attention. Nevertheless, several important classes of finite rings give rise to interesting geometries. In this paper we bring together some results, scattered over the literature, concerning finite rings and plane projective geometry over such rings. It doesn't contain new material, but by collecting stuff in one place, we hope to stimulate further research in this area for at least another 50 years of Finite Geometry.

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