A quasivariety has the weak ES property when the epimorphisms between its finitely generated members are surjective. A characterization of quasivarieties with the weak ES property is obtained and a method for detecting failures of this property in quasivarieties with a near unanimity term and in congruence permutable varieties is given. It is also shown that under reasonable assumptions the weak ES property implies arithmeticity. In particular, every filtral variety with the weak ES property is a discriminator variety.
Epimorphisms between finitely generated algebras / L. Carai, M. Kurtzhals, T. Moraschini. - In: INDAGATIONES MATHEMATICAE. - ISSN 0019-3577. - (2025), pp. 1-19. [10.1016/j.indag.2025.04.006]
Epimorphisms between finitely generated algebras
L. Carai
;T. Moraschini
2025
Abstract
A quasivariety has the weak ES property when the epimorphisms between its finitely generated members are surjective. A characterization of quasivarieties with the weak ES property is obtained and a method for detecting failures of this property in quasivarieties with a near unanimity term and in congruence permutable varieties is given. It is also shown that under reasonable assumptions the weak ES property implies arithmeticity. In particular, every filtral variety with the weak ES property is a discriminator variety.
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