## On $$\chi _{mub}$$-lattices and convex substructures of lattices and semilattices.(English)Zbl 0567.06006

The author investigates the following generalization of a lattice: The join of two elements is one of the minimal upper bounds given by a choice function. The meet is defined dually if maximal lower bounds exist and it is equal to the join otherwise. He gives a characterization of such structures arising from convex sublattices of a lattice or semilattice.
Reviewer: E.Fried

### MSC:

 06A06 Partial orders, general 06A12 Semilattices 06B05 Structure theory of lattices
Full Text:

### References:

 [1] E. Fried, E. T. Schmidt, Standard sublattices,Algebra Univ.,5 (1975), 203–211. · Zbl 0322.06008 [2] G. Grätzer,General lattice theory (Basel, 1978). · Zbl 0436.06001 [3] K.-M. Koh, On the lattice of convex sublattices of a lattice,Nanta Math.,5 (1972), 18–37. · Zbl 0284.06006 [4] K.-M. Koh, On sublattices of a lattice,Nanta, Math.,6 (1973), 68–79. · Zbl 0284.06005 [5] K. Leutola, J. Nieminen, Posets and generalized lattices,Algebra Univ.,16 (1983), 344–354. · Zbl 0514.06003 [6] J. Nieminen, On distributive and modular {$$\chi$$}-lattices,Yokohama Math. J.,31 (1983), 13–20. [7] J. Nieminen, The ideal structure of simple ternary algebras,Coll. Math.,40 (1978), 23–29. · Zbl 0415.06002 [8] M. Sholander, Medians and betweenness,Proc. Amer. Math. Soc.,5 (1954), 801–807. · Zbl 0056.26101
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.