The semiring of 1-preserving endomorphisms of a semilattice

Jaroslav Ježek; Tomáš Kepka

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 4, page 999-1003
  • ISSN: 0011-4642

Abstract

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We prove that the semirings of 1-preserving and of 0,1-preserving endomorphisms of a semilattice are always subdirectly irreducible and we investigate under which conditions they are simple. Subsemirings are also investigated in a similar way.

How to cite

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Ježek, Jaroslav, and Kepka, Tomáš. "The semiring of 1-preserving endomorphisms of a semilattice." Czechoslovak Mathematical Journal 59.4 (2009): 999-1003. <http://eudml.org/doc/37972>.

@article{Ježek2009,
abstract = {We prove that the semirings of 1-preserving and of 0,1-preserving endomorphisms of a semilattice are always subdirectly irreducible and we investigate under which conditions they are simple. Subsemirings are also investigated in a similar way.},
author = {Ježek, Jaroslav, Kepka, Tomáš},
journal = {Czechoslovak Mathematical Journal},
keywords = {semilattice; semiring; subdirectly irreducible; simple; semilattice; semiring; subdirectly irreducible},
language = {eng},
number = {4},
pages = {999-1003},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The semiring of 1-preserving endomorphisms of a semilattice},
url = {http://eudml.org/doc/37972},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Ježek, Jaroslav
AU - Kepka, Tomáš
TI - The semiring of 1-preserving endomorphisms of a semilattice
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 999
EP - 1003
AB - We prove that the semirings of 1-preserving and of 0,1-preserving endomorphisms of a semilattice are always subdirectly irreducible and we investigate under which conditions they are simple. Subsemirings are also investigated in a similar way.
LA - eng
KW - semilattice; semiring; subdirectly irreducible; simple; semilattice; semiring; subdirectly irreducible
UR - http://eudml.org/doc/37972
ER -

References

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  2. Bashir, R. El, Kepka, T., 10.1007/s00233-007-0725-7, Semigroup Forum 75 (2007), 588-608. (2007) Zbl1155.16034MR2353284DOI10.1007/s00233-007-0725-7
  3. Ježek, J., Kepka, T., Maróti, M., 10.1007/s00233-008-9045-9, Semigroup Forum 78 (2009), 253-261. (2009) MR2486638DOI10.1007/s00233-008-9045-9
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  5. McKenzie, R., McNulty, G., Taylor,, W., Algebras, Lattices, Varieties, Volume I, Wadsworth & Brooks/Cole, Monterey, CA (1987). (1987) MR0883644
  6. Mitchell, S. S., Fenoglio, P. B., 10.1007/BF02573125, Semigroup Forum 37 (1988), 79-91. (1988) Zbl0636.16020MR0929445DOI10.1007/BF02573125
  7. Monico, C., 10.1016/j.jalgebra.2003.09.034, J. Algebra 271 (2004), 846-854. (2004) Zbl1041.16041MR2025553DOI10.1016/j.jalgebra.2003.09.034
  8. Vandiver, H. S., 10.1090/S0002-9904-1934-06003-8, Bull. Amer. Math. Soc. 40 (1934), 916-920. (1934) MR1562999DOI10.1090/S0002-9904-1934-06003-8
  9. Zumbrägel, J., Classification of finite congruence-simple semirings with zero, Preprint. MR2431815

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