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A condition for modular lattices

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Abstract.

This paper proves that a geometric lattice of rank n is a modular lattice if its every maximal chain contains a modular element of rank greater than 1 and less than n. This result is generalized to a more general lattices of finite rank.

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Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, P. R. China

    Jun Wang & Jun Wu

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  1. Jun Wang
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  2. Jun Wu
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Correspondence to Jun Wang.

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Received November 8, 2005; accepted in final form April 3, 2007.

The first author is partially supported by the National Natural Science Foundation of China (Grant No. 10471016).

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Wang, J., Wu, J. A condition for modular lattices. Algebra univers. 57, 491–496 (2007). https://doi.org/10.1007/s00012-007-2064-7

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  • DOI: https://doi.org/10.1007/s00012-007-2064-7

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