# Article

 Title: Subalgebra extensions of partial monounary algebras (English) Author: Jakubíková-Studenovská, Danica Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 56 Issue: 3 Year: 2006 Pages: 845-855 Summary lang: English . Category: math . Summary: For a subalgebra ${\mathcal B}$ of a partial monounary algebra ${\mathcal A}$ we define the quotient partial monounary algebra ${\mathcal A}/{\mathcal B}$. Let ${\mathcal B}$, ${\mathcal C}$ be partial monounary algebras. In this paper we give a construction of all partial monounary algebras ${\mathcal A}$ such that ${\mathcal B}$ is a subalgebra of ${\mathcal A}$ and ${\mathcal C}\cong {\mathcal A}/{\mathcal B}$. (English) Keyword: partial monounary algebra Keyword: subalgebra Keyword: congruence Keyword: quotient algebra Keyword: subalgebra extension Keyword: ideal Keyword: ideal extension MSC: 08A55 MSC: 08A60 idZBL: Zbl 1164.08305 idMR: MR2261657 . Date available: 2009-09-24T11:38:37Z Last updated: 2020-07-03 Stable URL: http://hdl.handle.net/10338.dmlcz/128110 . Reference: [1] A. H. Clifford: Extensions of semigroup.Trans. Amer. Math. Soc. 68 (1950), 165–173. MR 0033836, 10.1090/S0002-9947-1950-0033836-2 Reference: [2] A. J. Hulin: Extensions of ordered semigroup.Czechoslovak Math. J. 26 (1976), 1–12. MR 0392740 Reference: [3] B. Jónsson: Topics in universal algebra.Springer-Verlag, Berlin, 1972. MR 0345895 Reference: [4] N. Kehayopulu and P. Kiriakuli: The ideal extension of lattices.Simon Stevin 64 (1990), 51–60. MR 1072483 Reference: [5] N. Kehayopulu and M. Tsingelis: The ideal extensions of ordered semigroups.Comm. Algebra 31 (2003), 4939–4969. MR 1998037, 10.1081/AGB-120023141 Reference: [6] J. Martinez: Torsion theory of lattice ordered groups.Czechoslovak Math. J. 25 (1975), 284–299. MR 0389705 Reference: [7] M. Novotný: Mono-unary algebras in the work of Czechoslovak mathematicians.Arch. Math. Brno 26 (1990), 155–164. MR 1188275 .

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