A Course in Universal Algebra

A Course in Universal Algebra, CIENCIAS EXATAS, Springer Nature B.V.

Sinopse

Universal algebra has enjoyed a particularly explosive growth in the last twenty years, and a student entering the subject now will find a bewildering amount of material to digest. This text is not intended to be
encyclopedic; rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests.
Chapter I contains a brief but substantial introduction to lattices, and to the close connection between complete lattices and closure operators. In particular, everything necessary for the subsequent study of congruence
lattices is included. Chapter II develops the most general and fundamental notions of uni­ versal algebra-these include the results that apply to all types of algebras, such as the homomorphism and isomorphism theorems. Free
algebras are discussed in great detail-we use them to derive the existence of simple algebras, the rules of equational logic, and the important Mal'cev conditions. We introduce the notion of classifying a variety by properties
of (the lattices of) congruences on members of the variety. Also, the center of an algebra is defined and used to characterize modules (up to polynomial equivalence). In Chapter III we show how neatly two famous results-the
refutation of Euler's conjecture on orthogonal Latin squares and Kleene's character­ ization of languages accepted by finite automata-can be presented using universal algebra. We predict that such "applied universal algebra"
will become much more prominent.

Metadado adicionado por UmLivro em 28/12/2024

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