Radicals and complete distributivity in relatively normal lattices

Jiří Rachůnek

Mathematica Bohemica (2003)

  • Volume: 128, Issue: 4, page 401-410
  • ISSN: 0862-7959

Abstract

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Lattices in the class ℐℛ𝒩 of algebraic, distributive lattices whose compact elements form relatively normal lattices are investigated. We deal mainly with the lattices in ℐℛ𝒩 the greatest element of which is compact. The distributive radicals of algebraic lattices are introduced and for the lattices in 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 M V -algebras, G M V -algebras and unital -groups.

How to cite

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Rachůnek, Jiří. "Radicals and complete distributivity in relatively normal lattices." Mathematica Bohemica 128.4 (2003): 401-410. <http://eudml.org/doc/249215>.

@article{Rachůnek2003,
abstract = {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.},
author = {Rachůnek, Jiří},
journal = {Mathematica Bohemica},
keywords = {relatively normal lattice; algebraic lattice; complete distributivity; closed element; radical; relatively normal lattice; algebraic lattice; complete distributivity; closed element; radical},
language = {eng},
number = {4},
pages = {401-410},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Radicals and complete distributivity in relatively normal lattices},
url = {http://eudml.org/doc/249215},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Rachůnek, Jiří
TI - Radicals and complete distributivity in relatively normal lattices
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 4
SP - 401
EP - 410
AB - 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.
LA - eng
KW - relatively normal lattice; algebraic lattice; complete distributivity; closed element; radical; relatively normal lattice; algebraic lattice; complete distributivity; closed element; radical
UR - http://eudml.org/doc/249215
ER -

References

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