The Annihilating-Ideal Graph of an Idealization

The Annihilating-Ideal Graph of an Idealization

The annihilating-ideal graph of a commutative ring R is denoted by AG ( R ) , whose vertices are all nonzero ideals of R with nonzero annihilators and two distinct vertices I and J are adjacent if and only if I J = 0 . In this paper, we consider the annihilating-ideal graphs of idealizations of comm...

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Veröffentlicht in:Iranian journal of science and technology. Transaction A, Science Science, 2017-03, Vol.41 (1), p.165-168
Hauptverfasser: Ahrari, M., Safari Sabet, Sh. A., Amini, B.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Apexes
Chemistry/Food Science
Earth Sciences
Engineering
Graphs
Life Sciences
Materials Science
Physics
Prime numbers
Research Paper
Rings (mathematics)
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Zusammenfassung:The annihilating-ideal graph of a commutative ring R is denoted by AG ( R ) , whose vertices are all nonzero ideals of R with nonzero annihilators and two distinct vertices I and J are adjacent if and only if I J = 0 . In this paper, we consider the annihilating-ideal graphs of idealizations of commutative rings. We study the behavior of the girth and diameter of the annihilating-ideal graph of a commutative ring when extending to idealizations of the ring.
ISSN:1028-6276
2364-1819
DOI:10.1007/s40995-017-0185-1