Geodesic
Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct
Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 27-43

Voir la notice de l'article provenant de la source Library of Science

Here we introduce the notion of strong quasi k-ideals of a semiring in SL⁺ and characterize the semirings that are distributive lattices of t-k-simple(t-k-Archimedean) subsemirings by their strong quasi k-ideals. A quasi k-ideal Q is strong if it is an intersection of a left k-ideal and a right k-ideal. A semiring S in SL⁺ is a distributive lattice of t-k-simple semirings if and only if every strong quasi k-ideal is a completely semiprime k-ideal of S. Again S is a distributive lattice of t-k-Archimedean semirings if and only if √Q is a k-ideal, for every strong quasi k-ideal Q of S.
Keywords: quasi k-ideal, strong quasi k-ideal, strong quasi k-simple, t-k-simple, t-k-Archimedean 
@article{DMGAA_2014_34_1_a1,
     author = {Bhuniya, Anjan and Jana, Kanchan},
     title = {Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {27--43},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a1/}
}
TY  - JOUR
AU  - Bhuniya, Anjan
AU  - Jana, Kanchan
TI  - Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2014
SP  - 27
EP  - 43
VL  - 34
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a1/
LA  - en
ID  - DMGAA_2014_34_1_a1
ER  - 
%0 Journal Article
%A Bhuniya, Anjan
%A Jana, Kanchan
%T Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct
%J Discussiones Mathematicae. General Algebra and Applications
%D 2014
%P 27-43
%V 34
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a1/
%G en
%F DMGAA_2014_34_1_a1
Bhuniya, Anjan; Jana, Kanchan. Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct. Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 27-43. http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a1/