Abstract
Many important classes of algebras, among them groups, rings, and lattices, consist of all the homomorphic images of certain ‘free’ algebras in the class, which are essentially determined by the cardinal of a free generating set. These are the varieties of algebras, which form the subject of Chapter IV, but free algebras are also of importance in more general situations, and we therefore devote a chapter to the study of properties of free algebras which are independent of the notion of a variety. A free algebra is itself a special case of the notion of a universal functor in category theory, and so we shall first describe universal functors in general categories (cf. Samuel [48], MacLane [63]).
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© 1981 D. Reidel Publishing Company, Dordrecht, Holland
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Cohn, P.M. (1981). Free Algebras. In: Universal Algebra. Mathematics and Its Applications, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8399-1_3
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DOI: https://doi.org/10.1007/978-94-009-8399-1_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-1254-7
Online ISBN: 978-94-009-8399-1
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