Geodesic
Radicals and complete distributivity in relatively normal lattices
Mathematica Bohemica, Tome 128 (2003) no. 4, pp. 401-410.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Lattices in the class $\mathcal{IRN}$ of algebraic, distributive lattices whose compact elements form relatively normal lattices are investigated. We deal mainly with the lattices in $\mathcal{IRN}$ the greatest element of which is compact. The distributive radicals of algebraic lattices are introduced and for the lattices in $\mathcal{IRN}$ with the sublattice of compact elements satisfying the conditional join-infinite distributive law they are compared with two other kinds of radicals. Connections between complete distributivity of algebraic lattices and the distributive radicals are described. The general results can be applied e.g. to $MV$-algebras, $GMV$-algebras and unital $\ell $-groups.
DOI : 10.21136/MB.2003.134005
Classification : 06D15, 06D20, 06D35, 06F05, 06F15
Keywords: relatively normal lattice; algebraic lattice; complete distributivity; closed element; radical 
@article{10_21136_MB_2003_134005,
     author = {Rach\r{u}nek, Ji\v{r}{\'\i}},
     title = {Radicals and complete distributivity in relatively normal lattices},
     journal = {Mathematica Bohemica},
     pages = {401--410},
     publisher = {mathdoc},
     volume = {128},
     number = {4},
     year = {2003},
     doi = {10.21136/MB.2003.134005},
     mrnumber = {2032477},
     zbl = {1052.06009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134005/}
}
TY  - JOUR
AU  - Rachůnek, Jiří
TI  - Radicals and complete distributivity in relatively normal lattices
JO  - Mathematica Bohemica
PY  - 2003
SP  - 401
EP  - 410
VL  - 128
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134005/
DO  - 10.21136/MB.2003.134005
LA  - en
ID  - 10_21136_MB_2003_134005
ER  - 
%0 Journal Article
%A Rachůnek, Jiří
%T Radicals and complete distributivity in relatively normal lattices
%J Mathematica Bohemica
%D 2003
%P 401-410
%V 128
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134005/
%R 10.21136/MB.2003.134005
%G en
%F 10_21136_MB_2003_134005
Rachůnek, Jiří. Radicals and complete distributivity in relatively normal lattices. Mathematica Bohemica, Tome 128 (2003) no. 4, pp. 401-410. doi : 10.21136/MB.2003.134005. http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134005/

Cité par Sources :