Jakubíková-Studenovská, Danica On pseudovarieties of monounary algebras. (English) Zbl 1258.08003 Asian-Eur. J. Math. 5, No. 1, Paper No. 3, 10 p. (2012). Algebras with one unary operation are called monounary algebras. A class of finite algebras is called a pseudovariety if it is closed under subalgebras, homomorphic images and direct products of finitely many members. A pseudovariety \({\mathcal P}\) is called equational if there exists a variety \({\mathcal V}\) such that \({\mathcal P}\) consists of all finite members of \({\mathcal V}\). A constructive description of the members of all pseudovarieties of monounary algebras is given. That description uses finite products, homomorphisms and subalgebras. It is shown that every equational pseudovariety of monounary algebras is finitely generated; moreover, if this pseudovariety is not the pseudovariety of all monounary algebras, it can be generated by a single algebra. Reviewer: G. I. Zhitomirskij (Herzliyya) Cited in 3 Documents MSC: 08A60 Unary algebras 08B99 Varieties Keywords:monounary algebra; pseudovariety; homomorphism; subalgebra; direct product PDFBibTeX XMLCite \textit{D. Jakubíková-Studenovská}, Asian-Eur. J. Math. 5, No. 1, Paper No. 3, 10 p. (2012; Zbl 1258.08003) Full Text: DOI References: [1] Almeida J., Series in Algebra 3, in: Finite Semigroups and Universal Algebra (1994) [2] Chvalina J., Functional Graphs, Quasiordered Sets and Commutative Hypergroups (1995) [3] Denecke K., Thai J. Math. 1 pp 1– [4] DOI: 10.1016/0001-8708(76)90029-3 · Zbl 0351.20035 · doi:10.1016/0001-8708(76)90029-3 [5] Graczyńska E., Bull. Sect. Logic Univ. Lódź 24 pp 215– [6] DOI: 10.2307/2311743 · Zbl 0117.26003 · doi:10.2307/2311743 [7] Jakubková-Studenovská D., Czechoslovak Math. J. 38 pp 256– [8] Jónsson B., Topics in Universal Algebra (1972) · Zbl 0225.08001 · doi:10.1007/BFb0058648 [9] DOI: 10.1051/ita:2003018 · Zbl 05424951 · doi:10.1051/ita:2003018 [10] Novotný M., Arch. Math. (Brno) 26 pp 155– [11] DOI: 10.1007/s11202-006-0044-3 · doi:10.1007/s11202-006-0044-3 [12] Skornjakov L. A., Colloq. Math Soc. János Bolyai 29 pp 735– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.