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Injective Hulls of Semilattices

Published online by Cambridge University Press:  20 November 2018

G. Bruns  and
H. Lakser
G. Bruns
Affiliation:
McMaster University, Hamilton, Ontario
H. Lakser
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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A (meet-) semilattice is an algebra with one binary operation ∧, which is associative, commutative and idempotent. Throughout this paper we are working in the category of semilattices. All categorical or general algebraic notions are to be understood in this category. In every semilattice S the relation

defines a partial ordering of S. The symbol "∨" denotes least upper bounds under this partial ordering. If it is not clear from the context in which partially ordered set a least upper bound is taken, we add this set as an index to the symbol; for example, ∨AX denotes the least upper bound of X in the partially ordered set A.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 115 - 118
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Cohn, P. M., Universal algebra, Harper and Row, 1965.Google Scholar