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On the least separative congruence on a semigroup. (English) Zbl 0535.20038

The paper announces new results on separative congruences (i.e. congruences \(\sim\) such that \(a^ 2\sim ab\sim b^ 2\) implies \(a\sim b)\) on a semigroup.

MSC:

20M10 General structure theory for semigroups
20M15 Mappings of semigroups
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References:

[1] Brinckmann, J.,Über das Radikal in potenzverbundenen Halbgruppen, Beiträge zur Algebra und Geometrie18 (1984), 49–61. · Zbl 0541.20042
[2] Cherubini, A. and A. Varisco,Quasi commutative semigroups and {\(\delta\)}-reflexive semigroups, Semigroup Forum19 (1980), 313–321. · Zbl 0432.20053 · doi:10.1007/BF02572524
[3] Chrislock, J.L.,On medial semigroups, J. Algebra12 (1969), 1–9. · Zbl 0187.29102 · doi:10.1016/0021-8693(69)90013-1
[4] Clifford, A.H., and G.B. Preston,The algebraic theory of semigroups, Vol. I, Amer. Math. Soc., Providence, Rhode Island, 1961. · Zbl 0111.03403
[5] Hoehnke, H.-J.,Structure of semigroups, Canad. J. Math.18 (1966), 449–491. · Zbl 0149.02402 · doi:10.4153/CJM-1966-048-1
[6] Hoehnke, H.-J.,Über das untere und obere Radikal einer Halbgruppe, Math. Z.89 (1965), 300–311. · Zbl 0201.36102 · doi:10.1007/BF01112162
[7] Mukherjee, N.P.,Quasi commutative semigroups.I, Czechoslovak Math. J.22 (1972), 449–453.
[8] Nagy, A.,The least separative congruence on a completely symmetrical semigroup, K. Marx Univ. Economics, Dept. Math., Budapest, 1980–4, 13–17.
[9] Nagy, A.,The least separative congruence on a weakly commutative semigroup, Czechoslovak Math. J.32 (1982), 630–632. · Zbl 0508.20034
[10] Pondelicek, B.,On weakly commutative semigroups, Czechoslovak Math. J.25 (1975), 20–25. · Zbl 0307.20039
[11] Roiz, E.N., and B.M. Schein,Radicals of semigroups, Semigroup Forum16 (1978), 299–344. · Zbl 0393.20047 · doi:10.1007/BF02194633
[12] Sedlock, J.T.,Green’s relation on a periodic semigroup, Czechoslovak Math. J.19 (1969), 318–323. · Zbl 0214.03504
[13] Strecker, R.,Über das Radikal {\(\chi\)}-kommutativer Halbgruppen, Math. Nachr.68 (1975), 49–57. · Zbl 0333.20049 · doi:10.1002/mana.19750680104
[14] Tamura, T., and J. Shafer,On exponential semigroups.I, Proc. Japan Acad.48 (1972), 77–80. · Zbl 0251.20063 · doi:10.3792/pja/1195519758
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