|
Every semigroup is isomorphic to a transitive semigroup of binary relations
Author(s):
Ralph
McKenzie;
Boris
M.
Schein
Journal:
Trans. Amer. Math. Soc.
349
(1997),
271-285.
MSC (1991):
Primary 20M30, 20M10;
Secondary 03G15, 04A05, 05C12, 08A02, 20M12, 20M20
MathSciNet review:
1370647
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Every (finite) semigroup is isomorphic to a transitive semigroup of binary relations (on a finite set).
References:
- 1.
- D. A. Bredihin and B. M. Schein, Representations of ordered semigroups and lattices by binary relations, Colloquium Mathematicum 39 (1978), 1-12. MR 80c:20093
- 2.
- A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. Vol. I, American Mathematical Society, Providence, R. I., 1961. MR 24:A2627
- 3.
- D. Rees, Note on semi-groups, Proceedings of the Cambridge Philosophical Society 37 (1941), 434-435. MR 3:199b
- 4.
- B. M. Xa'032n, Predstavlenie polugrupp pri pomowi binarnyh otnoxeni'032, Matematicheski'032 Sbornik 60 (1963), 293-303 [B. M. Schein, Representation of semigroups by means of binary relations, Matematicheski[??]i Sbornik 60 (1963), 292-303]. MR 27:3721
- 5.
- B. M. Schein, A new representation theorem on completely
![$[0]$](/tran/1997-349-01/S0002-9947-97-01708-X/gif-references/img1385.gif) -simple semigroups, Semigroup Forum 4 (1972), 312-320. MR 47:6923 - 6.
- B. M. Schein, Representation of involuted semigroups by binary relations, Fundamenta Mathematicæ 82 (1974), 121-141. MR 50:2381
- 7.
- A. K. Suxkevich, Teori'037 De'032stvi'037, kak Obwa'037 Teori'037 Grupp, Vorone'031, 1922
[A. K. Suschkewitsch, ``Theory of Operation as the General Theory of Groups,'' Voronezh, 1922]. - 8.
- A. K. Suschkewitsch, Über die endlichen Gruppen ohne das Gesetz der eindeutigen Umkehrbarkeit, Mathematische Annalen 99 (1928), 30-50.
- 9.
- K. A. Zarecki'032, Predstavlenie upor '037dochennyh polugrupp binarnymi otnoxeni'037mi, Izvesti'037 Vysxih Uchebnyh Zavedeni'032, Matematika 1959, no. 6(13), 48-50
[K. A. Zaretski[??]i, Representation of ordered semigroups by binary relations, Izvestiya Vysshikh Uchebnykh Zavedeni[??]i, Matematika 1959, no. 6(13), 48-50]. MR 24:A2630
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (1991):
20M30, 20M10,
03G15, 04A05, 05C12, 08A02, 20M12, 20M20
Retrieve articles in all Journals with
MSC (1991):
20M30, 20M10,
03G15, 04A05, 05C12, 08A02, 20M12, 20M20
Additional Information:
Ralph
McKenzie
Affiliation:
Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, Tennessee 37240
Email:
mckenzie@math.vanderbilt.edu
Boris
M.
Schein
Affiliation:
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Email:
bschein@uafsysb.uark.edu
DOI:
10.1090/S0002-9947-97-01708-X
PII:
S 0002-9947(97)01708-X
Keywords:
Semigroup of binary relations,
labeled multigraph,
transitive representation
Received by editor(s):
September 20, 1995
Additional Notes:
The first author was supported in part by NSF Grant No. DMS--9596043.
Copyright of article:
Copyright
1997,
American Mathematical Society
|
