Homomorphic images of finite subdirectly irreducible unary algebras

Jaroslav Ježek; P. Marković; David Stanovský

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 2, page 671-677
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Ježek, Jaroslav, Marković, P., and Stanovský, David. "Homomorphic images of finite subdirectly irreducible unary algebras." Czechoslovak Mathematical Journal 57.2 (2007): 671-677. <http://eudml.org/doc/31153>.

@article{Ježek2007,
abstract = {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.},
author = {Ježek, Jaroslav, Marković, P., Stanovský, David},
journal = {Czechoslovak Mathematical Journal},
keywords = {subdirectly irreducible unary algebra},
language = {eng},
number = {2},
pages = {671-677},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homomorphic images of finite subdirectly irreducible unary algebras},
url = {http://eudml.org/doc/31153},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Ježek, Jaroslav
AU - Marković, P.
AU - Stanovský, David
TI - Homomorphic images of finite subdirectly irreducible unary algebras
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 2
SP - 671
EP - 677
AB - 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.
LA - eng
KW - subdirectly irreducible unary algebra
UR - http://eudml.org/doc/31153
ER -

References

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  2. 10.1007/s00012-002-8192-1, Algebra Universalis 47 (2002), 319–327. (2002) MR1918733DOI10.1007/s00012-002-8192-1
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  4. A note on subdirectly irreducible groupoids, Acta Univ. Carolinae Math. Phys. 22 (1981), 25–28. (1981) Zbl0481.08001MR0635974
  5. On a class of groupoids, Acta Univ. Carolinae Math. Phys. 22 (1981), 29–49. (1981) Zbl0481.08002MR0635975
  6. Algebras, Lattices, Varieties, Volume  I, Wadsworth & Brooks/Cole, Monterey, 1987. (1987) MR0883644
  7. Every quasigroup is isomorphic to a subdirectly irreducible quasigroup modulo its monolith, Acta Sci. Math. (Szeged) 72 (2006), 59–64. (2006) MR2249239
  8. Homomorphic images of subdirectly irreducible groupoids, Comment. Math. Univ. Carolinae 42 (2001), 443–450. (2001) MR1859591
  9. 10.2307/2315275, Am. Math. Mon. 74 (1967), 957–960. (1967) Zbl0153.33802MR0228293DOI10.2307/2315275

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