| Title:
|
Subalgebras and homomorphic images of algebras having the CEP and the WCIP (English) |
| Author:
|
Walendziak, Andrzej |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
155-160 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with the WCIP is closed under the formation of homomorphic images. (English) |
| Keyword:
|
CEP |
| Keyword:
|
WCIP |
| Keyword:
|
weak congruence |
| Keyword:
|
lattice |
| MSC:
|
08A30 |
| MSC:
|
08B10 |
| idZBL:
|
Zbl 1049.08002 |
| idMR:
|
MR2040227 |
| . |
| Date available:
|
2009-09-24T11:10:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127872 |
| . |
| Reference:
|
[1] E. W. Kiss, L. Marki, P. Pröhle and W. Tholen: Categorical algebraic properties. A compendium on amalgamation, congruence extension, epimorphism, residual smallness and injectivity.Studia Sci. Math. Hung. 18 (1983), 79–141. MR 0759319 |
| Reference:
|
[2] B. Šešelja and G. Vojvodič: A note on some lattice characterizations of Hamiltonian groups.Univ. u Novom Sadu, Zb. Rad. Prirod-Mat. Fak. Ser. Mat. 19 (1989), 179–184. MR 1100270 |
| Reference:
|
[3] B. Šešelja and G. Vojvodič: CEP and homomorphic images of algebras.Univ. u Novom Sadu, Zb. Rad. Prirod-Mat. Fak. Ser. Mat. 19 (1989), 75–80. MR 1099995 |
| Reference:
|
[4] B. Šešelja and A. Tepavčevič: Weak congruences and homomorphisms.Univ. u Novom Sadu, Zb. Rad. Prirod-Mat. Fak. Ser. Mat. 20 (1990), 61–69. MR 1158426 |
| Reference:
|
[5] B. Šešelja and A. Tepavčevič: Special elements of the lattice and lattice identities.Univ. u Novom Sadu, Zb. Rad. Prirod-Mat. Fak. Ser. Mat. 20 (1990), 21–29. MR 1158422 |
| Reference:
|
[6] B. Šešelja and A. Tepavčevič: On CEP and semimodularity in the lattice of weak congruences.Univ. u Novom Sadu, Zb. Rad. Prirod-Mat. Fak. Ser. Mat. 22 (1992), 95–106. MR 1295228 |
| Reference:
|
[7] G. Vojvodič and B. Šešelja: On the lattice of weak congruence relations.Algebra Universalis 25 (1988), 121–130. MR 0950740, 10.1007/BF01229965 |
| . |
