We introduce the k-radicals of Green's relations in semirings with a semilattice additive reduct, introduce the notion of left k-regular (right k-regular) semirings and characterize these semirings by k-radicals of Green's relations. We also characterize the semirings which are distributive lattices of left k-simple subsemirings by k-radicals of Green's relations.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1198,
author = {Tapas Kumar Mondal and Anjan Kumar Bhuniya},
title = {On k-radicals of Green's relations in semirings with a semilattice additive reduct},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {33},
year = {2013},
pages = {85-93},
zbl = {1288.16060},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1198}
}
Tapas Kumar Mondal; Anjan Kumar Bhuniya. On k-radicals of Green's relations in semirings with a semilattice additive reduct. Discussiones Mathematicae - General Algebra and Applications, Tome 33 (2013) pp. 85-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1198/
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