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Finitely generated left commutative semigroups are residually finite. (English) Zbl 0525.20046


MSC:

20M10 General structure theory for semigroups
20M05 Free semigroups, generators and relations, word problems
20M14 Commutative semigroups
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References:

[1] Carlisle, W.H.,Residual Finiteness of Finitely Generated Commutative Semigroups, Pacific J. Math., 36 (1971), 99–101. · Zbl 0188.05703
[2] Clifford, A.H., and G.B. Preston,Algebraic Theory of Semigroups, Amer. Math. Soc. Surveys no. 7, Providence, R.I., 1961. · Zbl 0111.03403
[3] Evans, T.,Some Connections Between Residual Finiteness, Finite Embeddability and the Word Problem, J. London Math. Soc., 21 (1969), 399–403. · Zbl 0184.03502 · doi:10.1112/jlms/s2-1.1.399
[4] Evans, T.,Approximating Algebras by Finite Algebras, Part II, prepublication manuscript.
[5] Lallement, G.,On a Theorem of Malcev, Proc. Amer. Math. Soc., 30 (1971), 49–54. · Zbl 0234.20032 · doi:10.1090/S0002-9939-1971-0285646-8
[6] Malcev, A.I.,On Homorphisms Onto Finite Groups, Uch. Zap. Ivanovsk Pedagogm Inst., 18 (1958), 49–60.
[7] Nordahl, T.E.,Medial Semigroups, Thesis, University of California, 1974.
[8] Schein, B.M.,Homorphisms and Subdirect Product Decomposition of Semigroups, Pacific J. Math. 17 (1966), 529–547. · Zbl 0197.01603
[9] Eilenberg, S. and M.P. Schützenberger,Rational Sets in Commutative Monoids, J. Algebra, 13 (1969), 173–191. · Zbl 0206.02703 · doi:10.1016/0021-8693(69)90070-2
[10] Freyd, P.,Finiteness Theorem for Commutative Semigroups, Proc. Amer. Math. Soc. 19 (1968) p. 1003. · Zbl 0191.01703
[11] Rédei, L.,The Theory of Finitely Generated Commutative Semigroups, Oxford Univ. Press, New York, 1965.
[12] Schein, B.M.,On the theory of restrictive semigroups (in Russian), Izvestija Vysŝih Uĉebnyh Zavedeniî, Mathematika 1963, no. 2, 152–154.
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