Geodesic
A note on orthodox additive inverse semirings
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 149-154 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We show in an additive inverse regular semiring $(S, +, \cdot )$ with $E^{\bullet }(S)$ as the set of all multiplicative idempotents and $E^+(S)$ as the set of all additive idempotents, the following conditions are equivalent: (i) For all $e, f \in E^{\bullet }(S)$, $ef \in E^+(S)$ implies $fe\in E^+(S)$. (ii) $(S, \cdot )$ is orthodox. (iii) $(S, \cdot )$ is a semilattice of groups. This result generalizes the corresponding result of regular ring.
We show in an additive inverse regular semiring $(S, +, \cdot )$ with $E^{\bullet }(S)$ as the set of all multiplicative idempotents and $E^+(S)$ as the set of all additive idempotents, the following conditions are equivalent: (i) For all $e, f \in E^{\bullet }(S)$, $ef \in E^+(S)$ implies $fe\in E^+(S)$. (ii) $(S, \cdot )$ is orthodox. (iii) $(S, \cdot )$ is a semilattice of groups. This result generalizes the corresponding result of regular ring.
Classification : 16A78, 16E50, 16Y60, 20M07, 20M10
Keywords: additive inverse semirings; regular semirings; orthodox semirings 
@article{AUPO_2004_43_1_a15,
     author = {Sen, M.~K. and Maity, S.~K.},
     title = {A note on orthodox additive inverse semirings},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {149--154},
     year = {2004},
     volume = {43},
     number = {1},
     mrnumber = {2124613},
     zbl = {1067.16070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2004_43_1_a15/}
}
TY  - JOUR
AU  - Sen, M. K.
AU  - Maity, S. K.
TI  - A note on orthodox additive inverse semirings
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2004
SP  - 149
EP  - 154
VL  - 43
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AUPO_2004_43_1_a15/
LA  - en
ID  - AUPO_2004_43_1_a15
ER  - 
%0 Journal Article
%A Sen, M. K.
%A Maity, S. K.
%T A note on orthodox additive inverse semirings
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2004
%P 149-154
%V 43
%N 1
%U http://geodesic.mathdoc.fr/item/AUPO_2004_43_1_a15/
%G en
%F AUPO_2004_43_1_a15
Sen, M. K.; Maity, S. K. A note on orthodox additive inverse semirings. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 149-154. http://geodesic.mathdoc.fr/item/AUPO_2004_43_1_a15/