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Free inverse semigroups are not finitely presentable

Free inverse semigroups are not finitely presentable Acta Mathematiea Academiae Scientiarum Hung aricae Tomus 26 (1--2), (1975), 41--52o FREE INVERSE SEMIGROUPS ARE NOT FINITELY PRESENTABLE By B. M. SCHEIN (Saratov) In the memory of Professor A. Kert&z Free inverse semigroups became a subject of intense studies in the last few years. Their existence was proved long ago: as algebras with two operations (binary multiplication and unary involution) inverse semigroups may be characterized by a finite system of identities, i.e. they form a variety of algebras [10]. Therefore, free inverse semigroups do exist. A construction of a free algebra in a variety of algebras (as a quotient algebra of an absolutely free word algebra) is well known. Free inverse semigroups in such a form were considered by V. V. VAO_',,~ER [14] who found certain properties of such semigroups. A monogenic free inverse semigroup (i.e. a free inverse semigroup with one generator) was described by L. M. GLUSKIN [2]. Later this semigroup was described by H. E. SCHEIBLICH in a slightly different form [8]. The most essential progress in this direction was made in a paper [9] by H. E. SCHEIBLlCrI who described arbitrary free inverse semigroups. A relevant paper [1] by C. EBERHART and J. SELDEN should http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Academiae Scientiarum Hungarica Springer Journals

Free inverse semigroups are not finitely presentable

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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general
ISSN
0001-5954
eISSN
1588-2632
DOI
10.1007/BF01895947
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Abstract

Acta Mathematiea Academiae Scientiarum Hung aricae Tomus 26 (1--2), (1975), 41--52o FREE INVERSE SEMIGROUPS ARE NOT FINITELY PRESENTABLE By B. M. SCHEIN (Saratov) In the memory of Professor A. Kert&z Free inverse semigroups became a subject of intense studies in the last few years. Their existence was proved long ago: as algebras with two operations (binary multiplication and unary involution) inverse semigroups may be characterized by a finite system of identities, i.e. they form a variety of algebras [10]. Therefore, free inverse semigroups do exist. A construction of a free algebra in a variety of algebras (as a quotient algebra of an absolutely free word algebra) is well known. Free inverse semigroups in such a form were considered by V. V. VAO_',,~ER [14] who found certain properties of such semigroups. A monogenic free inverse semigroup (i.e. a free inverse semigroup with one generator) was described by L. M. GLUSKIN [2]. Later this semigroup was described by H. E. SCHEIBLICH in a slightly different form [8]. The most essential progress in this direction was made in a paper [9] by H. E. SCHEIBLlCrI who described arbitrary free inverse semigroups. A relevant paper [1] by C. EBERHART and J. SELDEN should

Journal

Acta Mathematica Academiae Scientiarum Hungarica – Springer Journals

Published: May 21, 2016

References

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