Starting with the most basic notions, Universal Algebra:
Fundamentals and Selected Topics introduces all the key elements
needed to read and understand current research in this field. Based
on the author's two-semester course, the text prepares students for
research work by providing a solid grounding in the fundamental
constructions and concepts of universal algebra and by introducing
a variety of recent research topics.
The first part of the book focuses on core components, including
subalgebras, congruences, lattices, direct and subdirect products,
isomorphism theorems, a clone of operations, terms, free algebras,
Birkhoff's theorem, and standard Maltsev conditions. The second
part covers topics that demonstrate the power and breadth of the
subject. The author discusses the consequences of Jonsson's lemma,
finitely and nonfinitely based algebras, definable principal
congruences, and the work of Foster and Pixley on primal and
quasiprimal algebras. He also includes a proof of Murski 's theorem
on primal algebras and presents McKenzie's characterization of
directly representable varieties, which clearly shows the power of
the universal algebraic toolbox. The last chapter covers the
rudiments of tame congruence theory.
Throughout the text, a series of examples illustrates concepts
as they are introduced and helps students understand how universal
algebra sheds light on topics they have already studied, such as
Abelian groups and commutative rings. Suitable for newcomers to the
field, the book also includes carefully selected exercises that
reinforce the concepts and push students to a deeper understanding
of the theorems and techniques.
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