Compactness of systems of equations on completely regular semigroups



: Harju T, Karhumaki J, Petrich M

Publisher: SPRINGER-VERLAG BERLIN

: 1997

: Lecture Notes in Computer Science

: STRUCTURES IN LOGIC AND COMPUTER SCIENCE

: LECT NOTES COMPUT SC

: 1261

: 268

: 280

: 13

: 0302-9743


A semigroup S is said to have the compactness property, or CP for short, if each system of equations over a finite set of variables has an equivalent finite subsystem, that is, having exactly the same solutions in S. We prove that a completely 0-simple semigroup S satisfies CP if and only if the group G in a Rees matrix representation S = M-0(I, G, Lambda; P) satisfies this property. Further, a variety of completely regular semigroups in which the finitely generated members have finite matrices is shown to satisfy CP if and only if the corresponding variety of groups satisfies CP. It is then shown that the varieties of bands of groups satisfy the condition on finite matrices.



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