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Proceedings of the American Mathematical Society

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Semimodular posets and the Jordan-Dedekind chain condition

Authors: L. Haskins and S. Gudder
Journal: Proc. Amer. Math. Soc. 28 (1971), 395-396
MSC: Primary 06.20
MathSciNet review: 0276144
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Abstract: In this paper it is shown that an upper semimodular poset without infinite chains satisfies the Jordan-Dedekind chain condition. This corrects an error in Theorem 14, p. 40 of [1] and generalizes that theorem.

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  • [1] Garrett Birkhoff, Lattice theory, Third edition. American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053

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Keywords: Semimodular posets, Jordan-Dedekind chain condition, partially ordered sets, lattices
Article copyright: © Copyright 1971 American Mathematical Society