We present a classification of those finite length modules X over a ring A which are isomorphic to every module Y of the same length such that Ker(HomA(−, X)) = Ker(HomA(−, Y )), i.e. X is determined by its length and the torsion pair cogenerated by X. We also prove the dual result using the torsion pair generated by X. For A right hereditary, we prove an analogous classification using the coto...

Let R be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph of R , denoted by ξR, is a graph whose vertex set is the of allnon-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacentif and only if either Ann(I) ⊆ J or Ann(J) ⊆ I. In this paper, we investigate the basicproperties of the graph ξR. In particular, we showthat ξR is a connected grap...

An Osmium sensitizer and anthracene annihilator are incorporated into a metal ion linked multilayer photoanode that harnesses NIR light in an integrated triplet–triplet annihilation upconversion solar cell.

We construct a generator system of the annihilator of a generalized Verma module of a reductive Lie algebra induced from a character of a parabolic subalgebra as an analogue of the minimal polynomial of a matrix.

§1.1. Motivation. The purpose of these notes is to explain the definition and basic properties of the Néron model A of an abelian variety A over a global or local field K. We also give some idea of the proof that the Néron model exists. In the context of Faltings’s proof of Mordell’s conjecture, the primary motivation for doing so is that the notion of the Faltings height hF (A) will be defined...

Problem 1.(The Mapping Cone is a Homotopy Limit and a Homotopy Colimit) Let A be an Abelian category. Let A● and B● be objects in Ch●(A). Let f ● ∶ A● → B● be a morphism in Ch●(A). For every object T ● of Ch●(A), a left homotopy annihilator to T ● is a pair (Q●, σ●) of a morphism Q● ∶ B● → T ● in Ch●(A) and a nullhomotopy (σn ∶ An → T n−1)n∈Z of Q● ○ f ●, i.e., for every n ∈ Z, Q ○ f = dn−1 T ○...

LFSR-based stream ciphers with nonlinear filters or combiners are susceptible to algebraic attacks using linearization methods to solve an overdefined system of nonlinear equations. And this process is greatly enhanced if the filtering or combining function has a low degree annihilator. To prevent such an attack, one would choose the parameters of that function so that the degree of its annihil...