A torsion theory is called differential (higher differential) if a derivation (higher derivation) can be extended from any module to the module of quotients corresponding to the torsion theory. We study conditions equivalent to higher differentiability of a torsion theory. It is known that the Lambek, Goldie and any perfect torsion theories are differential. We show that these classes of torsio...

Let R be a ring and U be a Lie ideal of R. Suppose that σ, τ are endomorphisms of R. A family D = {d n } n ∈ N of additive mappings d n :R → R is said to be a (σ,τ)- higher derivation of U into R if d 0 = I R , the identity map on R and [Formula: see text] holds for all a, b ∈ U and for each n ∈ N. A family F = {f n } n ∈ N of additive mappings f n :R → R is said to be a generalized (σ,τ)- high...

Let $A$ be a Banach ternary algebra over a scalar field $Bbb R$ or $Bbb C$ and $X$ be a ternary Banach $A$--module. Let $sigma,tau$ and $xi$ be linear mappings on $A$, a linear mapping $D:(A,[~]_A)to (X,[~]_X)$ is called a Lie ternary $(sigma,tau,xi)$--derivation, if $$D([a,b,c])=[[D(a)bc]_X]_{(sigma,tau,xi)}-[[D(c)ba]_X]_{(sigma,tau,xi)}$$ for all $a,b,cin A$, where $[abc]_{(sigma,tau,xi)}=ata...

In this paper, we introduce and discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module.

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of (α, β)-derivation to (α, β)higher derivation and demonstrate that a filter of a hereditary torsion theory that is invariant for α and β is (α, β)-higher derivation invariant. As a consequence, any higher derivation can be extended from a module to its module of quotients. Then...

Ordinary t-timed modular Petri Nets are used for modeling, analysis, synthesis and performance evaluation of random topology dedicated production systems. Each system is first decomposed into production line, assembly, disassembly and parallel machine modules followed by derivation of their modular Petri Net models. Two sets of modules, generic and generalized respectively, are derived correspo...

Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, we have obtained the Postnikov-like approximation of a module, with the help of a suitable set of morphisms.