A right ideal A of a ring R is called annihilator-small if A+ T = R; T a right ideal, implies that l(T ) = 0; where l( ) indicates the left annihilator. The sum Ar of all such right ideals turns out to be a two-sided ideal that contains the Jacobson radical and the left singular ideal, and is contained in the ideal generated by the total of the ring. The ideal Ar is studied, conditions when it ...

Let G be a real semisimple group. There are two important invariants associated with the equivalence class of an irreducible unitary representation of G, namely, the associated variety of the annihilator in the universal enveloping algebra and Howe’s N -spectrum where N is a nilpotent subgroup of G. The associated variety is defined in a purely algebraic way. The N spectrum is defined analytica...

assume that $(n,l)$, is a pair of finite dimensional nilpotent lie algebras, in which $l$ is non-abelian and $n$ is an ideal in $l$ and also $mathcal{m}(n,l)$ is the schur multiplier of the pair $(n,l)$. motivated by characterization of the pairs $(n,l)$ of finite dimensional nilpotent lie algebras by their schur multipliers (arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

In [15], Kaplansky introduced Baer rings as rings in which every right (left) annihilator ideal is generated by an idempotent. According to Clark [9], a ring R is called quasi-Baer if the right annihilator of every right ideal is generated (as a right ideal) by an idempotent. Further works on quasi-Baer rings appear in [4, 6, 17]. Recently, Birkenmeier et al. [8] called a ring R to be a right (...

Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

In this paper, we present an application of Variable Pulse Width Finite Rate of Innovation (VPW-FRI) in dealing with multichannel Electrocardiogram (ECG) data using a common annihilator. By extending the conventional FRI model to include additional parameters such as pulse width and asymmetry, VPWFRI has been able to deal with a more general class of pulses. The common annihilator, which is int...

Let φ : Rm → Rd be a map of free modules over a commutative ring R. Fitting’s Lemma shows that the “Fitting ideal,” the ideal of d × d minors of φ, annihilates the cokernel of φ and is a good approximation to the whole annihilator in a certain sense. In characteristic 0 we define a Fitting ideal in the more general case of a map of graded free modules over a Z/2graded skew-commutative algebra a...

An element a of a semigroup algebra F[S] over a field F is called a right annihilating element of F[S] if xa = 0 for every x ∈ F[S], where 0 denotes the zero of F[S]. The set of all right annihilating elements of F[S] is called the right annihilator of F[S]. In this paper we show that, for an arbitrary field F, if a finite semigroup S is a direct product or semilattice or right zero semigroup o...