Accosiative rings and algebras are very interesting algebraic
structures. In a strict sense, the theory of algebras (in particular,
noncommutative algebras) originated fromasingleexample,
namelythequaternions, createdbySirWilliamR.Hamilton in1843.
Thiswasthe?rstexampleofanoncommutative"numbersystem". During
thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative
algebras, began to bring some order into them and to single out certain
types of algebras for special attention. Thus, low-dimensional algebras,
division algebras, and commutative algebras, were classi?ed and
characterized. The ?rst complete results in the structure theory of
associative algebras over the real and complex ?elds were obtained by
T.Molien, E.Cartan and G.Frobenius. Modern ring theory began when
J.H.Wedderburn proved his celebrated cl- si?cation theorem for ?nite
dimensional semisimple algebras over arbitrary ?elds. Twenty years
later, E.Artin proved a structure theorem for rings satisfying both the
ascending and descending chain condition which generalized Wedderburn
structure theorem. The Wedderburn-Artin theorem has since become a corn-
stone of noncommutative ring theory. The purpose of this book is to
introduce the subject of the structure theory of associative rings. This
book is addressed to a reader who wishes to learn this topic from the
beginning to research level. We have tried to write a self-contained
book which is intended to be a modern textbook on the structure theory
of associative rings and related structures and will be accessible for
independent study.
