Abstract
AbstractIn universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to polynomial equations, inside congruence permutable varieties, and with respect to term equations, among all algebras of size two and all algebras of size three with a cyclic automorphism. Furthermore, for each size at least three, we prove that, modulo term equivalence, there is a continuum of equational domains of that size.
Publisher
Springer Science and Business Media LLC
Reference46 articles.
1. Aglianò, P., Baker, K.A.: Congruence properties of two-generated varieties. In: Contributions to General Algebra 12 (Vienna, 1999), pp. 71–83. Heyn, Klagenfurt (2000)
2. Ágoston, I., Demetrovics, J., Hannák, L.: On the number of clones containing all constants (a problem of R. McKenzie). In: Lectures in universal algebra (Szeged, 1983), Colloq. Math. Soc. János Bolyai, vol. 43, pp. 21–25. North-Holland Publishing Company, Amsterdam (1986)
3. Aichinger, E.: The polynomial functions of certain algebras that are simple modulo their center. In: Contributions to General Algebra, vol. 17, pp. 9–24. Heyn, Klagenfurth (2006)
4. Aichinger, E.: Constantive Mal’cev clones on finite sets are finitely related. Proc. Am. Math. Soc. 138(10), 3501–3507 (2010). https://doi.org/10.1090/S0002-9939-2010-10395-7
5. Aichinger, E., Cannon, G.A., Ecker, J., Kabza, L., Neuerburg, K.: Some near-rings in which all ideals are intersections of Noetherian quotients. Rocky Mt. J. Math. 38(3), 713–726 (2008). https://doi.org/10.1216/RMJ-2008-38-3-713