Linear Orders on General Algebras |
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Authors: | Email author" target="_blank">Sándor?RadeleczkiEmail author Jen??Szigeti |
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Institution: | (1) Institute of Mathematics, University of Miskolc, Miskolc, 3515, Hungary |
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Abstract: | We answer the question, when a partial order in a partially ordered algebraic structure has a compatible linear extension.
The finite extension property enables us to show, that if there is no such extension, then it is caused by a certain finite
subset in the direct square of the base set. As a consequence, we prove that a partial order can be linearly extended if and
only if it can be linearly extended on every finitely generated subalgebra. Using a special equivalence relation on the above
direct square, we obtain a further property of linearly extendible partial orders. Imposing conditions on the lattice of compatible
quasi orders, the number of linear orders can be determined. Our general approach yields new results even in the case of semi-groups
and groups. |
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Keywords: | Primary 06F99 06F05 Secondary 08A05 06D15 |
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