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Compactness of systems of equations on completely regular semigroups
Tekijät: Harju T, Karhumaki J, Petrich M
Kustantaja: SPRINGER-VERLAG BERLIN
Julkaisuvuosi: 1997
Lehti:: Lecture Notes in Computer Science
Tietokannassa oleva lehden nimi: STRUCTURES IN LOGIC AND COMPUTER SCIENCE
Lehden akronyymi: LECT NOTES COMPUT SC
Vuosikerta: 1261
Aloitussivu: 268
Lopetussivu: 280
Sivujen määrä: 13
ISSN: 0302-9743
Tiivistelmä
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.
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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