Notes on sectionally complemented lattices. I

被引：0
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作者：
G. Grätzer
H. Lakser
机构：
[1] Department of Mathematics,
[2] University of Manitoba,undefined
[3] Department of Mathematics,undefined
[4] University of Manitoba,undefined
来源：
Acta Mathematica Hungarica | 2005年 / 108卷
关键词：
relative complement; free lattice; uniquely complemented;
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摘要：
In 1944, R.P. Dilworth proved (unpublished) that every finite distributive lattice D can be represented as the congruence lattice of a finite lattice L. In 1960, G. Grätzer and E. T. Schmidt improved this result by constructing a finite  sectionally complemented lattice L whose congruence lattice represents D. In L, sectional complements do not have to be unique. The one sectional complement constructed by G. Grätzer and E. T. Schmidt in 1960, we shall call the 1960 sectional complement. This paper examines it in detail. The main result is an algebraic characterization of the 1960 sectional complement.
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页码：117 / 127
页数：10
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