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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.

Some defective secant varieties to osculating varieties of Veronese surfaces.

Alessandra Bernardi, Maria Virginia Catalisano (2006)

Collectanea Mathematica

We consider the k-osculating varietiesOk,d to the Veronese d?uple embeddings of P2. By studying the Hilbert function of certain zero-dimensional schemes Y ⊂ P2, we find the dimension of Osk,d, the (s?1)th secant varieties of Ok,d, for 3 ≤ s ≤ 6 and s = 9, and we determine whether those secant varieties are defective or not.

Some homological properties of amalgamated modules along an ideal

Hanieh Shoar, Maryam Salimi, Abolfazl Tehranian, Hamid Rasouli, Elham Tavasoli (2023)

Czechoslovak Mathematical Journal

Let R and S be commutative rings with identity, J be an ideal of S , f : R → S be a ring homomorphism, M be an R -module, N be an S -module, and let ϕ : M → N be an R -homomorphism. The amalgamation of R with S along J with respect to f denoted by R ⋈ f J was introduced by M. D’Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of ( R ⋈ f J ) -module called the amalgamation of M and N along J with respect to ϕ , and denoted by M ⋈ ϕ J N . We study some homological properties of the ( R ⋈ f J ) -module M ⋈ ϕ J N . Among other results,...

Some notes on the composite G -valuations

Angeliki Kontolatou (1994)

Archivum Mathematicum

In analogy with the notion of the composite semi-valuations, we define the composite G -valuation v from two other G -valuations w and u . We consider a lexicographically exact sequence ( a , β ) : A u → B v → C w and the composite G -valuation v of a field K with value group B v . If the assigned to v set R v = { x ∈ K / v ( x ) ≥ 0 or v ( x ) non comparable to 0 } is a local ring, then a G -valuation w of K into C w is defined with its assigned set R w a local ring, as well as another G -valuation u of a residue field is defined with G -value group A u .

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