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Modular and Admissible Semilattices
Published online by Cambridge University Press: 20 November 2018
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We correct some errors in [1] and extend some of the results there. Generally, we shall follow the terminology and notation of [1]. There is an error in the proof of Lemma 3.13 there, and consequently the subsequent results which depend on it are incorrect as stated. However, they are correct if we replace the condition “a-admissible” by “strongly a-admissible” (see [3] where this notion was introduced). We also show that the results in [1] are correct if the semilattices are assumed to be modular.
We shall change the terminology in [3] slightly.
Definition 1 (see [3]). Let A be a Boolean algebra and let D be a meet semilattice with 1. An admissible map f.A X D → D is called strongly admissible if
where a’ is the complement of a in A.
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- Research Article
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- Copyright © Canadian Mathematical Society 1984
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