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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the relationship between AP, RS and CEP


Author: Keith A. Kearnes
Journal: Proc. Amer. Math. Soc. 105 (1989), 827-839
MSC: Primary 08B10; Secondary 03C05, 03G99, 08B25, 20M07
MathSciNet review: 952317
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Abstract: We prove that in a residually small congruence modular variety the amalgamation property implies the commutator condition $ {\text{R}}$. A consequence of this is that, for all congruence modular varieties, $ {\text{AP + RS}}$ implies the CEP. We also show that this implication holds for any variety of semigroups.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0952317-5
PII: S 0002-9939(1989)0952317-5
Article copyright: © Copyright 1989 American Mathematical Society