| Title:
|
The semiring of 1-preserving endomorphisms of a semilattice (English) |
| Author:
|
Ježek, Jaroslav |
| Author:
|
Kepka, Tomáš |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
999-1003 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
semilattice |
| Keyword:
|
semiring |
| Keyword:
|
subdirectly irreducible |
| Keyword:
|
simple |
| MSC:
|
06A12 |
| MSC:
|
16Y60 |
| idZBL:
|
Zbl 1224.06007 |
| idMR:
|
MR2563572 |
| . |
| Date available:
|
2010-07-20T15:53:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140531 |
| . |
| Reference:
|
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| Reference:
|
[2] Bashir, R. El, Kepka, T.: Congruence-simple semirings.Semigroup Forum 75 (2007), 588-608. Zbl 1155.16034, MR 2353284, 10.1007/s00233-007-0725-7 |
| Reference:
|
[3] Ježek, J., Kepka, T., Maróti, M.: The endomorphism semiring of a semilattice.Semigroup Forum 78 (2009), 253-261. MR 2486638, 10.1007/s00233-008-9045-9 |
| Reference:
|
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| Reference:
|
[5] McKenzie, R., McNulty, G., Taylor,, W.: Algebras, Lattices, Varieties, Volume I.Wadsworth & Brooks/Cole, Monterey, CA (1987). MR 0883644 |
| Reference:
|
[6] Mitchell, S. S., Fenoglio, P. B.: Congruence-free commutative semirings.Semigroup Forum 37 (1988), 79-91. Zbl 0636.16020, MR 0929445, 10.1007/BF02573125 |
| Reference:
|
[7] Monico, C.: On finite congruence-simple semirings.J. Algebra 271 (2004), 846-854. Zbl 1041.16041, MR 2025553, 10.1016/j.jalgebra.2003.09.034 |
| Reference:
|
[8] Vandiver, H. S.: Note on a simple type of algebras in which the cancellation law of addition does not hold.Bull. Amer. Math. Soc. 40 (1934), 916-920. MR 1562999, 10.1090/S0002-9904-1934-06003-8 |
| Reference:
|
[9] Zumbrägel, J.: Classification of finite congruence-simple semirings with zero.Preprint. MR 2431815 |
| . |
