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Completely meet-irreducible tolerances in distributive Noetherian lattices. (English) Zbl 0682.06010
A lattice L is Noetherian if it satisfies the Ascending Chain Condition. It is proven that for a distributive Noetherian lattice L, the set of all completely meet-irreducible tolerances in Tol L (the lattices of all tolerances on L) is o-isomorphic to the set of all intervals in the poset of all meet-irreducible elements of L.
Reviewer: I.Chajda

MSC:
06F10 Noether lattices
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References:
[1] G. Birkhoff: Lattice theory. 3rd Amer. Math. Soc., Providence 1979. · Zbl 0505.06001
[2] J. Niederle: A note on tolerance lattices. Časop. pěst. matem. 107 (1982), 221-224. · Zbl 0502.08004
[3] J. Niederle: On skeletal and irreducible elements in tolerance lattices of finite distributive lattices. Časop. pěst. matem. 107 (1982), 23-29. · Zbl 0484.06015
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