Geodesic
Basis properties for semigroups
Glasgow mathematical journal, Tome 30 (1988) no. 1, pp. 101-109

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A universal algebra A is said to have the basis property (BP) if any two minimal generating sets (bases) for a subalgebra of A have the same cardinality. This property was studied by the author for inverse semigroups in [5, 6]. For instance free inverse semigroups have BP. When treated as universal algebras, a classical theorem of linear algebra states that vector spaces have BP. In this paper we study BP for semigroups. 
Jones, Peter R. Basis properties for semigroups. Glasgow mathematical journal, Tome 30 (1988) no. 1, pp. 101-109. doi: 10.1017/S0017089500007072
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