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The algebra whose elements are congruence classes of an algebra and whose basic operations are induced on those classes by compatibility of the congruence.
burris-universal-algebraEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Congruence compatibility is precisely what makes the value of every induced operation independent of the selected representatives of its input classes.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
burris-universal-algebraThis is an authored directed relation from the source endpoint to the target endpoint.
Given an algebra and a congruence , identify and exactly when ; each basic operation is then defined on the resulting -classes.
Identify elements by a stated equivalence relation and equip the quotient with the induced structure. The edge detail must state the representatives and equivalence relation.
burris-universal-algebraEach relation below starts at this concept.
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