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Название: A Course in Universal Algebra
Авторы: Burris S., Sankappanavar H.
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 universal 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).