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The study of algebraic structures and properties applying to large classes of such structures. For example, ideas from group theory and ring theory are extended and considered for structures with other signatures (systems of basic or fundamental operations).
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Parametrization of topological algebraic objects
Please regard this as a tentative answer since I am not sure that it corresponds to the spirit of your query. Many of the situations that you use to illustrate your query can be coded by using the co …