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Books > Science & Mathematics > Mathematics > Algebra
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Algebras, Lattices, Varieties, Volume I (Hardcover)
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Algebras, Lattices, Varieties, Volume I (Hardcover)
Series: AMS Chelsea Publishing
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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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