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Strictly locally order affine complete lattices

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Abstract

We call a latticeL strictly locally order-affine complete if, given a finite subsemilatticeS ofL n, every functionf: S →L which preserves congruences and order, is a polynomial function. The main results are the following: (1) all relatively complemented lattices are strictly locally order-affine complete; (2) a finite modular lattice is strictly locally order-affine complete if and only if it is relatively complemented. These results extend and generalize the earlier results of D. Dorninger [2] and R. Wille [9, 10].

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Authors and Affiliations

  1. Department of Mathematics, Tartu University, EE2400, Tartu, Estonia

    Kalle Kaarli & Karin Täht

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  1. Kalle Kaarli
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  2. Karin Täht
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Communicated by G. Grätzer

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Kaarli, K., Täht, K. Strictly locally order affine complete lattices. Order 10, 261–270 (1993). https://doi.org/10.1007/BF01110547

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  • DOI: https://doi.org/10.1007/BF01110547

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