English

Semigroups By E. S. Ljapin

The present book has the goal of setting forth the basic aspects of the algebraic theory of semigroups. A semigroup (or in other words an associative system) is a set considered with respect to a binary associative operation defined in it. The concept of a semigroup is so simple and natural that it is hard to say when it first appeared. As Klein points out, there were doubts, even in the period when the theory of groups was formulated as a separate mathematical discipline, as to whether that which we call a semigroup should be taken as the fundamental concept. However, the problems facing mathematics at that stage of its development made it necessary to choose a more restrictive concept, that of a group. One of the most important reasons that the theory of groups played so large a role in the ensuing development of mathematics was that the algebraic theory of groups by its very nature was the abstract study of invertible transformations. The need for considering such mappings occurs in such diverse fields of mathematics, that one encounters the concept and properties of groups in very many mathematical (and not only mathematical) disciplines. In spite of the importance and fruitfulnes

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