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Completions of semilattices of cancellative semigroups

Published online by Cambridge University Press:  18 May 2009

W. D. Burgess
Affiliation:
University of Ottawa, OttawaCanadaKin 9B4
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K. Shoji has pointed out to me that construction [1] does not always yield a completion. In the notation of [1], the homomorphism from the strong semilattice of cancellative semigroups S to its purported completion T in Abian's order is not always a monomorphism. The difficulty arises when there is eɛ E, e=sup{eEe'<e>e} but {‐e,e'}e' is not faithful, i.e. there are x, y with x¬y in Se such that φe,e'(x)=φe,e'(y) for all e'<e. A modification of the construction saves all parts of Theorem 1 except the fact that the new embedding ST need not preserve suprema existing in S; it does if S is a semilattice of groups. The sequel [2] also needs amodification in the form of an additional hypothesis.

Type
Corrigendum
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCE

Burgess, W. D., Completions of semilattices of cancellative semigroups, Glasgow Math J. 21 (1980), 2937.Google Scholar
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