E-varieties of regular semigroups,relatively bifree objects and fully invariant congruences |
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Authors: | Monica Mangold |
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Institution: | (1) Department of Mathematics, Monash University, 3168 Clayton, Victoria, Australia |
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Abstract: | Analogous to the concept of a free object on a setX in a variety of algebras is the notion of a bifree object onX in an e-variety of regular semigroups. If an e-variety contains a bifree object onX, then a homomorphic image of that bifree object is itself bifree onX in some e-variety if and only if the corresponding congruence is fully invariant. Furthermore, the lattice of e-subvarieties
of any locally inverse or E-solid e-variety ε is antiisomorphic with the lattice of all fully invariant congruences on the
bifree object on a countably infinite setX in ε. We give a Birkhoff-type theorem for classes of locally inverse or E-solid semigroups, and we give an intrinsic test
for whether or not a regular semigroup is bifree onX in the e-variety it generates. |
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Keywords: | 20 M 17 |
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