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This book is the third of a three-volume set of books on the theory
of algebras, a study that provides a consistent framework for
understanding algebraic systems, including groups, rings, modules,
semigroups and lattices. Volume I, first published in the 1980s,
built the foundations of the theory and is considered to be a
classic in this field. The long-awaited volumes II and III are now
available. Taken together, the three volumes provide a
comprehensive picture of the state of art in general algebra today,
and serve as a valuable resource for anyone working in the general
theory of algebraic systems or in related fields. The two new
volumes are arranged around six themes first introduced in Volume
I. Volume II covers the Classification of Varieties, Equational
Logic, and Rudiments of Model Theory, and Volume III covers Finite
Algebras and their Clones, Abstract Clone Theory, and the
Commutator. These topics are presented in six chapters with
independent expositions, but are linked by themes and motifs that
run through all three volumes.
This book is the second of a three-volume set of books on the
theory of algebras, a study that provides a consistent framework
for understanding algebraic systems, including groups, rings,
modules, semigroups and lattices. Volume I, first published in the
1980s, built the foundations of the theory and is considered to be
a classic in this field. The long-awaited volumes II and III are
now available. Taken together, the three volumes provide a
comprehensive picture of the state of art in general algebra today,
and serve as a valuable resource for anyone working in the general
theory of algebraic systems or in related fields. The two new
volumes are arranged around six themes first introduced in Volume
I. Volume II covers the Classification of Varieties, Equational
Logic, and Rudiments of Model Theory, and Volume III covers Finite
Algebras and their Clones, Abstract Clone Theory, and the
Commutator. These topics are presented in six chapters with
independent expositions, but are linked by themes and motifs that
run through all three volumes.
This book presents the foundations of a general theory of algebras.
Often called ``universal algebra'', this theory provides a common
framework for all algebraic systems, including groups, rings,
modules, fields, and lattices. Each chapter is replete with useful
illustrations and exercises that solidify the reader's
understanding. The book begins by developing the main concepts and
working tools of algebras and lattices, and continues with examples
of classical algebraic systems like groups, semigroups, monoids,
and categories. The essence of the book lies in Chapter 4, which
provides not only basic concepts and results of general algebra,
but also the perspectives and intuitions shared by practitioners of
the field. The book finishes with a study of possible uniqueness of
factorizations of an algebra into a direct product of directly
indecomposable algebras. There is enough material in this text for
a two semester course sequence, but a one semester course could
also focus primarily on Chapter 4, with additional topics selected
from throughout the text.
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