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Before tackling the question in my title I should perhaps begin by saying what a semigroup is. A non-empty set S endowed with a single binary operation . is called a semigroup if, for all x , y , z in S ,

This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into the theories of minimal ideals in a semi group, inverse semi groups, simple semi groups, congruences on a semi group, and the embedding of a semi group in a group. Among the more important recent developments of which an extended treatment is presented are B. M. Sain's theory of the representations of an arbitrary semi group by partial one-to-one transformations of a set, L. Redei's theory of finitely generated commutative semi groups, J. M. Howie's theory of amalgamated free products of semi groups, and E. J. Tully's theory of representations of a semi group by transformations of a set. Also a full account is given of Malcev's theory of the congruences on a full transformation semi group.

The algebraic theory of semigroups

1. Words D. Perrin 2. Square free words and idempotent semigroups J. Berstel and C. Reutenauer 3. Van der Waerden's theorem J. E. Pin 4. Repetitive mappings and morphisms G. Pirillo 5. Factorizations of free monoids D. Perrin 6. Subwords J. Sakarovitch and I. Simon 7. Unavoidable irregularities in words M. P. Schutzenberger 8. The critical factorization theorem Choffrut 9. Equations in words 10. Rearrangements of words D. Foata 11. Words and trees R. Cori.

Before tackling the question in my title I should perhaps begin by saying what a semigroup is. A non-empty set S endowed with a single binary operation . is called a semigroup if, for all x , y , z in S ,

References

The algebraic theory of semigroups

Combinatorics on words

Introduction to Semigroup Theory

Semigroups and combinatorial applications

Theory of codes

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