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Let be an ideal of a commutative Noetherian ring and be a nonnegative integer. Let and be two finitely generated -modules. In certain cases, we give some bounds under inclusion for the annihilators of and in terms of minimal primary decomposition of the zero submodule of , 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.
Let be a commutative ring with identity and be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of is defined as the graph with the vertex set and two distinct vertices and are adjacent if and only if and . In this paper, the perfectness of for some classes of rings is investigated.
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.
Let and be commutative rings with identity, be an ideal of , be a ring homomorphism, be an -module, be an -module, and let be an -homomorphism. The amalgamation of with along with respect to denoted by was introduced by M. D’Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of -module called the amalgamation of and along with respect to , and denoted by . We study some homological properties of the -module . Among other results,...
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