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Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings

Mitra Jalali, Abolfazl Tehranian, Reza Nikandish, Hamid Rasouli (2020)

Commentationes Mathematicae Universitatis Carolinae

Let R be a commutative ring with identity and A ( R ) be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of R is defined as the graph SAG ( R ) with the vertex set A ( R ) * = A ( R ) { 0 } and two distinct vertices I and J are adjacent if and only if I Ann ( J ) ( 0 ) and J Ann ( I ) ( 0 ) . In this paper, the perfectness of SAG ( R ) for some classes of rings R is investigated.

Sur les Extensions Triviales Commutatives

Farid Kourki (2009)

Annales mathématiques Blaise Pascal

Nous caractérisons les extensions triviales semiGoldie, de cogénération finie, mininjectives et quasi-Frobeniusiens. Comme application, nous montrons que tout anneau noethérien s’injecte dans un anneau quasi-Frobeniusien.

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