Commutative Semigroups

This is the first book about commutative semigroups in general. Emphasis is on structure but the other parts of the theory are at least surveyed and a full set of about 850 references is included. The book is intended for mathematicians who do research on semigroups or who encounter commutative semigroups in their research. Front Matter....Pages i-xiv Elementary Properties....Pages 1-28 Cancellative Semigroups....Pages 29-67 Semilattice Decompositions....Pages 69-93 Subdirect Decompositions....Pages 95-114 Group Coextensions....Pages 115-139 Finitely Generated Semigroups....Pages 141-163 Subcomplete Semigroups....Pages 165-186 Other Results....Pages 187-201 Nilsemigroups....Pages 203-226 Group-Free Semigroups....Pages 227-258 Subcomplete Semigroups....Pages 259-293 Commutative Semigroup Cohomology....Pages 295-326 The Overpath Method....Pages 327-360 Semigroups with Zero Cohomology....Pages 361-378 Back Matter....Pages 379-437