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 ...

Let $R$ be a commutative ring and $mathbb{A}(R)$ be the set of all ideals with non-zero annihilators. Assume that $mathbb{A}^*(R)=mathbb{A}(R)diagdown {0}$ and $mathbb{F}(R)$ denote the set of all finitely generated ideals of $R$. In this paper, we introduce and investigate the {it finitely generated subgraph} of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_F(R)$. It is the (undi...

We compare the K-theories of symplectic quotients with respect to a compact connected Lie group and with respect to its maximal torus, and in particular we give a method for computing the former in terms of the latter. More specifically, let G be a compact connected Lie group with no torsion in its fundamental group, let T be a maximal torus of G, and let M be a compact Hamiltonian G-space. Let...

We introduce a graph structure \(\Gamma^{\ast}_2(R)\) for commutative rings with unity. study some of the properties \(\Gamma^{\ast}_2(R)\). Also we parameters and find which is split.

let $r$ be a commutative ring with identity‎. ‎we use‎ ‎$varphi (r)$ to denote the comaximal ideal graph‎. ‎the vertices‎ ‎of $varphi (r)$ are proper ideals of r which are not contained‎ ‎in the jacobson radical of $r$‎, ‎and two vertices $i$ and $j$ are‎ ‎adjacent if and only if $i‎ + ‎j = r$‎. ‎in this paper we show some‎ ‎properties of this graph together with planarity of line graph‎ ‎assoc...