Geodesic
Regular additively inverse semirings
Acta mathematica Universitatis Comenianae, Tome 75 (2006) no. 1 
M. K. Sen; S. K. Maity. Regular additively inverse semirings. Acta mathematica Universitatis Comenianae, Tome 75 (2006) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2006_75_1_a12/
@article{AMUC_2006_75_1_a12,
     author = {M. K. Sen and S. K. Maity},
     title = {Regular additively inverse semirings},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2006},
     volume = {75},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2006_75_1_a12/}
}
TY  - JOUR
AU  - M. K. Sen
AU  - S. K. Maity
TI  - Regular additively inverse semirings
JO  - Acta mathematica Universitatis Comenianae
PY  - 2006
VL  - 75
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AMUC_2006_75_1_a12/
ID  - AMUC_2006_75_1_a12
ER  - 
%0 Journal Article
%A M. K. Sen
%A S. K. Maity
%T Regular additively inverse semirings
%J Acta mathematica Universitatis Comenianae
%D 2006
%V 75
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2006_75_1_a12/
%F AMUC_2006_75_1_a12

Voir la notice de l'article provenant de la source Comenius University

In this paper we show that in a regular additively inverse semiring ( S , +, × ) with 1 satisfying the conditions (A) a ( a + a' ) = a + a' ; (B) a ( b + b' ) = ( b + b' ) a , and (C) a + a ( b + b' ) = a , for all a, b Î S , the sum of two principal left ideals is again a principal left ideal. Also, we decompose S as a direct sum of two mutually inverse ideals.