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Modular and Admissible Semilattices

Published online by Cambridge University Press:  20 November 2018

C. S. Hoo  and
P. V. Ramana Murty
C. S. Hoo
Affiliation:
University of Alberta, Edmonton, Alberta
P. V. Ramana Murty
Affiliation:
Andhra University, Waltair, India
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 5 , 01 October 1984 , pp. 795 - 799
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Hoo, C. S., Pseudocomplemented and implicative semilattices, Can. J. Math. 35 (1982), 423–437.Google Scholar
2. Murtv, P V. Ramana, Prime and implicative semilattices. Algebra Universalis 10 (1980), 31–35.Google Scholar
3. Murty, P. V. Ramana and Rao, V. V. Rama, Characterization of certain classes of pseudocomplemented semilattices. Algebra Universalis 4 (1974), 289–300.Google Scholar
4. Murty, P. V. Ramana and Murty, M. Krishna, On admissible semilattices, Algebra Universalis 6 (1976), 355–366.Google Scholar