Geodesic
Multiplicatively Idempotent Semirings in which All Congruences Are Ideal
Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 376-383

Voir la notice de l'article provenant de la source Math-Net.Ru

The study of multiplicatively idempotent semirings with additional conditions is continued. It is proved that every multiplicatively idempotent semiring with ideal congruences is isomorphic to the direct product of a Boolean ring and a generalized Boolean lattice. Thus, a new abstract characterization is obtained for the direct products of Boolean rings and generalized Boolean lattices. Examples are given.
Keywords: semiring, multiplicatively idempotent semiring, ideal congruence, Boolean ring, generalized Boolean lattice. 
@article{MZM_2022_112_3_a5,
     author = {E. M. Vechtomov and A. A. Petrov},
     title = {Multiplicatively {Idempotent} {Semirings} in which {All} {Congruences} {Are} {Ideal}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {376--383},
     publisher = {mathdoc},
     volume = {112},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a5/}
}
TY  - JOUR
AU  - E. M. Vechtomov
AU  - A. A. Petrov
TI  - Multiplicatively Idempotent Semirings in which All Congruences Are Ideal
JO  - Matematičeskie zametki
PY  - 2022
SP  - 376
EP  - 383
VL  - 112
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a5/
LA  - ru
ID  - MZM_2022_112_3_a5
ER  - 
%0 Journal Article
%A E. M. Vechtomov
%A A. A. Petrov
%T Multiplicatively Idempotent Semirings in which All Congruences Are Ideal
%J Matematičeskie zametki
%D 2022
%P 376-383
%V 112
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a5/
%G ru
%F MZM_2022_112_3_a5
E. M. Vechtomov; A. A. Petrov. Multiplicatively Idempotent Semirings in which All Congruences Are Ideal. Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 376-383. http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a5/