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Some bounds for the annihilators of local cohomology and Ext modules

Ali Fathi (2022)

Czechoslovak Mathematical Journal

Let 𝔞 be an ideal of a commutative Noetherian ring R and t be a nonnegative integer. Let M and N be two finitely generated R -modules. In certain cases, we give some bounds under inclusion for the annihilators of Ext R t ( M , N ) and H 𝔞 t ( M ) in terms of minimal primary decomposition of the zero submodule of M , which are independent of the choice of minimal primary decomposition. Then, by using those bounds, we compute the annihilators of local cohomology and Ext modules in certain cases.

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 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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