On the finite embeddability property for residuated ordered groupoids

Blok, W.; van Alten, C.

doi:10.1090/S0002-9947-04-03654-2

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On the finite embeddability property for residuated ordered groupoids

Authors: W. J. Blok and C. J. van Alten
Journal: Trans. Amer. Math. Soc. 357 (2005), 4141-4157
MSC (2000): Primary 06F05; Secondary 03B47, 06F07, 06F99, 08C15, 08A50
Posted: October 7, 2004
MathSciNet review: 2159703
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Abstract: The finite embeddability property (FEP) for integral, commutative residuated ordered monoids was established by W. J. Blok and C. J. van Alten in 2002. Using Higman's finite basis theorem for divisibility orders we prove that the assumptions of commutativity and associativity are not required: the classes of integral residuated ordered monoids and integral residuated ordered groupoids have the FEP as well. The same holds for their respective subclasses of (bounded) (semi-)lattice ordered structures. The assumption of integrality cannot be dropped in general--the class of commutative, residuated, lattice ordered monoids does not have the FEP--but the class of -potent commutative residuated lattice ordered monoids does have the FEP, for any $n < \omega$ .

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