Article
Keywords:
subdirectly irreducible unary algebra
Summary:
We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty.
References:
[1] S. Bulman-Fleming, E. Hotzel, and J. Wang:
Semigroups that are factors of subdirectly irreducible semigroups by their monolith. Algebra Universalis 51 (2004), 1–7.
DOI 10.1007/s00012-004-1823-y |
MR 2067147
[3] T. Kepka:
On a class of subdirectly irreducible groupoids. Acta Univ. Carolinae Math. Phys. 22 (1981), 17–24.
MR 0635973 |
Zbl 0478.08005
[4] T. Kepka:
A note on subdirectly irreducible groupoids. Acta Univ. Carolinae Math. Phys. 22 (1981), 25–28.
MR 0635974 |
Zbl 0481.08001
[6] R. McKenzie, G. McNulty, and W. Taylor:
Algebras, Lattices, Varieties, Volume I. Wadsworth & Brooks/Cole, Monterey, 1987.
MR 0883644
[7] R. McKenzie, D. Stanovský:
Every quasigroup is isomorphic to a subdirectly irreducible quasigroup modulo its monolith. Acta Sci. Math. (Szeged) 72 (2006), 59–64.
MR 2249239
[8] D. Stanovský:
Homomorphic images of subdirectly irreducible groupoids. Comment. Math. Univ. Carolinae 42 (2001), 443–450.
MR 1859591