let $m_r$ be a module with $s=end(m_r)$. we call a submodule $k$ of $m_r$ annihilator-small if $k+t=m$, $t$ a submodule of $m_r$, implies that $ell_s(t)=0$, where $ell_s$ indicates the left annihilator of $t$ over $s$. the sum $a_r(m)$ of all such submodules of $m_r$ contains the jacobson radical $rad(m)$ and the left singular submodule $z_s(m)$. if $m_r$ is cyclic, then $a_r(m)$ is the unique ...

We study the exterior depth of an E-module and its exterior generic annihilator numbers. For the exterior depth of a squarefree E-module we show how it relates to the symmetric depth of the corresponding S-module and classify those simplicial complexes having a particular exterior depth in terms of their exterior shifting. We define exterior annihilator numbers analogously to the annihilator nu...

Consider real reductive group G, as defined in [Wal88]. Let Π be an irreducible admissible representation of G with the distribution character ΘΠ, [Har51]. Denote by uΠ the lowest term in the asymptotic expansion of ΘΠ, [BV80]. This is a finite linear combination of Fourier transforms of nilpotent coadjoint orbits, uΠ = ∑ O cOμ̂O. As shown by Rossmann, [Ros95], the closure of the union of the ni...

Throughout this paper, the ring R is not necessarily with an identity. We denote the set of all idempotents of R by E(R). Also, for a subset X ⊆ R, we denote the right (resp., left) annihilator of X in R by annr(X) (resp., ann (X)). Now, according to Fraser and Nicholson in [5], we call a ring R a left p.p.-ring, in brevity, l.p.p.-ring, if for all x ∈ R, there exists an idempotent e such that ...

The LOMOPLAN (LOcal MOnoPLane ANnihilator) lter in three dimensions is a deconvolution lter that takes a volume in and produces two volumes out. The x-output volume results from a rst order prediction-error lter on the x-axis, and the y-output volume is likewise on the y-axis. Synthetic data studies are promising.

We prove that the separating subspace for a derivation on a nonassociative //'-algebra is contained in the annihilator of the algebra. In particular, derivations on nonassociative H* -algebras with zero annihilator are continuous.

So far there is no systematic attempt to construct Boolean functions with maximum annihilator immunity. In this paper we present a construction keeping in mind the basic theory of annihilator immunity. This construction provides functions with the maximum possible annihilator immunity and the weight, nonlinearity and algebraic degree of the functions can be properly calculated under certain cas...

Spectra attacks proposed recently are more data efficient than algebraic attacks against stream cipher. They are also time-andspace efficient. A measurement of the security of a stream cipher against spectra attacks is spectral immunity, the lowest spectral weight of the annihilator of the key stream. We study both the annihilator and the spectral immunity. We obtain a necessary and sufficient ...