| Title:
|
Radical classes of distributive lattices having the least element (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
409-425 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathcal D$ be the system of all distributive lattices and let $\mathcal D_0$ be the system of all $L\in \mathcal D$ such that $L$ possesses the least element. Further, let $\mathcal D_1$ be the system of all infinitely distributive lattices belonging to $\mathcal D_0$. In the present paper we investigate the radical classes of the systems $\mathcal D$, $\mathcal D_0$ and $\mathcal D_1$. (English) |
| Keyword:
|
distributive lattice |
| Keyword:
|
infinite distributivity |
| Keyword:
|
radical class |
| MSC:
|
06D05 |
| MSC:
|
06D10 |
| idZBL:
|
Zbl 1007.06009 |
| idMR:
|
MR1931325 |
| DOI:
|
10.21136/MB.2002.134071 |
| . |
| Date available:
|
2009-09-24T22:03:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134071 |
| . |
| Reference:
|
[1] P. Conrad: $K$-radical classes of lattice ordered groups.Algebra, Proc. Conf. Carbondale (1980), Lecture Notes Math vol. 848, 1981, pp. 186–207. Zbl 0455.06010, MR 0613186 |
| Reference:
|
[2] P. F. Conrad, M. R. Darnel: Generalized Boolean algebras in lattice ordered groups.Order 14 (1998), 295–319. MR 1644504 |
| Reference:
|
[3] Dao-Rong Ton: Product radical classes of $\ell $-groups.Czechoslovak Math. J. 42 (1992), 129–142. MR 1152176 |
| Reference:
|
[4] M. Darnel: Closure operations on radicals of lattice ordered groups.Czechoslovak Math. J. 37 (1987), 51–64. MR 0875127 |
| Reference:
|
[5] J. Jakubík: Radical mappings and radical classes of lattice ordered groups.Symposia Math vol. 21, Academic Press, New York, 1977, pp. 451–477. MR 0491397 |
| Reference:
|
[6] J. Jakubík: Products of radical classes of lattice ordered groups.Acta Math. Univ. Comen. 39 (1980), 31–41. MR 0619260 |
| Reference:
|
[7] J. Jakubík: On $K$-radicals of lattice ordered groups.Czechoslovak Math. J. 33 (1983), 149–163. |
| Reference:
|
[8] J. Jakubík: On radical classes of abelian linearly ordered groups.Math. Slovaca 35 (1985), 141–154. MR 0795009 |
| Reference:
|
[9] J. Jakubík: Radical subgroups of lattice ordered groups.Czechoslovak Math. J. 36 (1986), 285–297. MR 0831316 |
| Reference:
|
[10] J. Jakubík: Closure operators on the lattice of radical classes of lattice ordered groups.Czechoslovak Math. J. 38 (1988), 71–77. MR 0925941 |
| Reference:
|
[11] J. Jakubík: $K$-radical classes of abelian linearly ordered groups.Math. Slovaca (1988), 33–44. MR 0945078 |
| Reference:
|
[12] J. Jakubík: On a radical class of lattice ordered groups.Czechoslovak Math. J. 39 (1989), 641–643. MR 1017999 |
| Reference:
|
[13] J. Jakubík: On torsion classes generated by radical classes of lattice ordered groups.Archivum Math. 26 (1990), 115–119. MR 1188270 |
| Reference:
|
[14] J. Jakubík: Closed convex $\ell $-subgroups and radical classes of convergence $\ell $-groups.Math. Bohem. 122 (1997), 301–315. MR 1600660 |
| Reference:
|
[15] J. Jakubík: Radical classes of generalized Boolean algebras.Czechoslovak Math. J. 48 (1998), 253–268. MR 1624315, 10.1023/A:1022885303504 |
| Reference:
|
[16] J. Jakubík: Radical classes of $MV$-algebras.Czechoslovak Math. J. 49 (1999), 191–211. MR 1676805, 10.1023/A:1022428713092 |
| Reference:
|
[17] J. Jakubík: Radical classes of complete lattice ordered groups.Czechoslovak Math. J. 49 (1999), 417–424. MR 1719676 |
| Reference:
|
[18] J. Jakubík, G. Pringerová: Radical classes of cyclically ordered groups.Math. Slovaca 38 (1998), 255–268. MR 0977904 |
| Reference:
|
[19] V. M. Kopytov, N. Ya. Medvedev: The Theory of Lattice-Ordered Groups.Kluwer Academic Publishers, Dordrecht, 1994. MR 1369091 |
| Reference:
|
[20] J. Martinez: Torsion theory for lattice-ordered groups.Czechoslovak Math. J. 25, 284–299. Zbl 0331.06009, MR 0389705 |
| Reference:
|
[21] N. Ya. Medvedev: On the lattice of radicals of a finitely generated $\ell $-group.Math. Slovaca 33 (1983), 185–188. (Russian) MR 0699088 |
| . |
