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Keywords:
groupoid; simple; paramedial
groupoid; simple; paramedial
Summary:
The study of paramedial groupoids (with emphasis on the structure of simple paramedial groupoids) was initiated in [1] and continued in [2], [3] and [5]. The aim of the present paper is to give a full description of finite simple zeropotent paramedial groupoids (i.e., of finite simple paramedial groupoids of type (II)—see [2]). A reader is referred to [1], [2], [3] and [7] for notation and various prerequisites.
References:
[1] J. R. Cho, J. Ježek and T. Kepka: Paramedial groupoids. Czechoslovak Math. J. 49(124) (1999), 277–290. DOI 10.1023/A:1022448218116 | MR 1692473
[2] J. R. Cho, J. Ježek and T. Kepka: Simple paramedial groupoids. Czechoslovak Math. J. 49(124) (1999), 391–399. DOI 10.1023/A:1022464621750 | MR 1692520
[3] R. El Bashir, J. Ježek and T. Kepka: Simple zeropotent paramedial groupoids are balanced. Czechoslovak Math. J. 50(125) (2000), 397–399. DOI 10.1023/A:1022435321907 | MR 1761396
[4] J. Ježek and T. Kepka: Medial groupoids. Rozpravy ČSAV, Řada mat. a přír. věd 93 (1983), 93. MR 0734873
[5] J. Ježek and T. Kepka: The equational theory of paramedial cancellation groupoids. Czechoslovak Math. J. 50(125) (2000), 25–34. DOI 10.1023/A:1022476800989 | MR 1745455
[6] J. Ježek and T. Kepka: Linear equational theories and semimodule representations. Internat. J. Algebra Comput. 8 (1998), 599–615. DOI 10.1142/S0218196798000284 | MR 1675018
[7] T. Kepka and P. Němec: Simple balanced groupoids. Acta Univ. Palackianae Olomoucensis, Fac. rer. mat., Mathematica 35 (1996), 53–60. MR 1485044
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