Geodesic
Studying semigroups using the properties of their prime $m$-ideals
The Bulletin of Irkutsk State University. Series Mathematics, Tome 34 (2020), pp. 109-125

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

In this article, we present the idea of $m$-ideals, prime $m$-ideals and their associated types for a positive integer $m$ in a semigroup. We present different chrarcterizations of semigroups through $m$-ideals. We demonstrate that the ordinary ideals, and their relevent types differ from the $m$-ideals and their assocated types by presenting concrete examples on the maximal, irreducible and strongly irreducible $m$-ideals. We conclude from the study that the introduction of the $m$-ideal will explore new fields of studies in semigroups and their applications.
Keywords: completely prime $m$-ideals, strongly prime $m$-ideals, maximal $m$-ideals, irreducible $m$-ideals, strongly Irreducible $m$-ideals. 
@article{IIGUM_2020_34_a7,
     author = {M. Munir and N. Kausar and B. Davvaz and M. Gulistan and M. Gulzar},
     title = {Studying semigroups using the properties of their prime $m$-ideals},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {109--125},
     publisher = {mathdoc},
     volume = {34},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2020_34_a7/}
}
TY  - JOUR
AU  - M. Munir
AU  - N. Kausar
AU  - B. Davvaz
AU  - M. Gulistan
AU  - M. Gulzar
TI  - Studying semigroups using the properties of their prime $m$-ideals
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2020
SP  - 109
EP  - 125
VL  - 34
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2020_34_a7/
LA  - en
ID  - IIGUM_2020_34_a7
ER  - 
%0 Journal Article
%A M. Munir
%A N. Kausar
%A B. Davvaz
%A M. Gulistan
%A M. Gulzar
%T Studying semigroups using the properties of their prime $m$-ideals
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2020
%P 109-125
%V 34
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIGUM_2020_34_a7/
%G en
%F IIGUM_2020_34_a7
M. Munir; N. Kausar; B. Davvaz; M. Gulistan; M. Gulzar. Studying semigroups using the properties of their prime $m$-ideals. The Bulletin of Irkutsk State University. Series Mathematics, Tome 34 (2020), pp. 109-125. http://geodesic.mathdoc.fr/item/IIGUM_2020_34_a7/