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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Locally equational completeness of rings and semigroups


Author: M. R. Chiaro
Journal: Proc. Amer. Math. Soc. 66 (1977), 189-193
MSC: Primary 08A20
DOI: https://doi.org/10.1090/S0002-9939-1977-0465981-6
MathSciNet review: 0465981
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Abstract: Hu has developed locally equational classes as a generalization of equational classes. It is shown here that the lattice of equational classes of rings is a proper sublattice of the lattice of locally equational classes of rings but the locally equationally complete rings are precisely the equationally complete rings. Using the equational and locally equational class operators the locally equationally complete classes of semigroups are shown to be those that are equationally complete.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0465981-6
Article copyright: © Copyright 1977 American Mathematical Society