A note on orthodox additive inverse semirings

@article{Sen2004,
abstract = {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.},
author = {Sen, M. K., Maity, S. K.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {additive inverse semirings; regular semirings; orthodox semirings; additive inverse semirings; regular semirings; orthodox semirings; idempotents},
language = {eng},
number = {1},
pages = {149-154},
publisher = {Palacký University Olomouc},
title = {A note on orthodox additive inverse semirings},
url = {http://eudml.org/doc/32346},
volume = {43},
year = {2004},
}

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
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 149
EP - 154
AB - 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.
LA - eng
KW - additive inverse semirings; regular semirings; orthodox semirings; additive inverse semirings; regular semirings; orthodox semirings; idempotents
UR - http://eudml.org/doc/32346
ER -