A1 Refereed original research article in a scientific journal
Compactness of systems of equations on completely regular semigroups
Authors: Harju T, Karhumaki J, Petrich M
Publisher: SPRINGER-VERLAG BERLIN
Publication year: 1997
Journal:: Lecture Notes in Computer Science
Journal name in source: STRUCTURES IN LOGIC AND COMPUTER SCIENCE
Journal acronym: LECT NOTES COMPUT SC
Volume: 1261
First page : 268
Last page: 280
Number of pages: 13
ISSN: 0302-9743
Abstract
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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