Geodesic
On the essential annihilating-ideal graph of commutative rings
Ars Mathematica Contemporanea, Tome 22 (2022) no. 3, article no. 05, 16 p.

Voir la notice de l'article provenant de la source Ars Mathematica Contemporanea website

Let R be a commutative ring with unity, A(R) be the set of all annihilating-ideals of R and A*(R) = A(R) \ {0}. In this paper, we introduced and studied the essential annihilating-ideal graph of R, denoted by EG(R), with vertex set A*(R) and two distinct vertices I1 and I2 are adjacent if and only if Ann(I1I2) is an essential ideal of R. We prove that EG(R) is a connected graph with diameter at most three and girth at most four if EG(R) contains a cycle. Furthermore, the rings R are characterized for which EG(R) is a star or a complete graph. Finally, we classify all the Artinian rings R for which EG(R) is isomorphic to some well-known graphs.
DOI : 10.26493/1855-3974.2645.8fc
Keywords: Annihilating-ideal graph, zero-divisor graph, complete graph, planar graph, genus of a graph 
@article{10_26493_1855_3974_2645_8fc,
     author = {Mohd Nazim and Nadeem ur Rehman},
     title = {On the essential annihilating-ideal graph of commutative rings},
     journal = {Ars Mathematica Contemporanea},
     eid = {05},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2022},
     doi = {10.26493/1855-3974.2645.8fc},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2645.8fc/}
}
TY  - JOUR
AU  - Mohd Nazim
AU  - Nadeem ur Rehman
TI  - On the essential annihilating-ideal graph of commutative rings
JO  - Ars Mathematica Contemporanea
PY  - 2022
VL  - 22
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2645.8fc/
DO  - 10.26493/1855-3974.2645.8fc
LA  - en
ID  - 10_26493_1855_3974_2645_8fc
ER  - 
%0 Journal Article
%A Mohd Nazim
%A Nadeem ur Rehman
%T On the essential annihilating-ideal graph of commutative rings
%J Ars Mathematica Contemporanea
%D 2022
%V 22
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2645.8fc/
%R 10.26493/1855-3974.2645.8fc
%G en
%F 10_26493_1855_3974_2645_8fc
Mohd Nazim; Nadeem ur Rehman. On the essential annihilating-ideal graph of commutative rings. Ars Mathematica Contemporanea, Tome 22 (2022) no. 3, article  no. 05, 16 p. doi : 10.26493/1855-3974.2645.8fc. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2645.8fc/

Cité par Sources :