Previous |  Up |  Next


partial monounary algebra; subalgebra; congruence; quotient algebra; subalgebra extension; ideal; ideal extension
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 ${\mathcal C}\cong {\mathcal A}/{\mathcal B}$.
[1] A. H. Clifford: Extensions of semigroup. Trans. Amer. Math. Soc. 68 (1950), 165–173. DOI 10.1090/S0002-9947-1950-0033836-2 | MR 0033836
[2] A. J. Hulin: Extensions of ordered semigroup. Czechoslovak Math. J. 26 (1976), 1–12. MR 0392740
[3] B. Jónsson: Topics in universal algebra. Springer-Verlag, Berlin, 1972. MR 0345895
[4] N. Kehayopulu and P. Kiriakuli: The ideal extension of lattices. Simon Stevin 64 (1990), 51–60. MR 1072483
[5] N. Kehayopulu and M. Tsingelis: The ideal extensions of ordered semigroups. Comm. Algebra 31 (2003), 4939–4969. DOI 10.1081/AGB-120023141 | MR 1998037
[6] J. Martinez: Torsion theory of lattice ordered groups. Czechoslovak Math. J. 25 (1975), 284–299. MR 0389705
[7] M. Novotný: Mono-unary algebras in the work of Czechoslovak mathematicians. Arch. Math. Brno 26 (1990), 155–164. MR 1188275
Partner of
EuDML logo