let $mathcal{a}$ be a banach algebra and $mathcal{m}$ be a banach $mathcal{a}$-bimodule. we say that a linear mapping $delta:mathcal{a} rightarrow mathcal{m}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{a} rightarrow mathcal{m}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{a}$. giving some facts concerning general...

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

‎In this paper‎, ‎algebraic investigations on sup-$Sigma$-algebras are presented‎. ‎A representation theorem for‎ ‎sup-$Sigma$-algebras in terms of nuclei and quotients is obtained‎. ‎Consequently‎, ‎the relationship between‎ ‎the congruence lattice of a sup-$Sigma$-algebra and the lattice of its nuclei is fully developed.

We define the notion of a piecewise linear map from fan $$\Sigma $$ to $$\tilde{\mathfrak {B}}(G)$$ , cone over Tits building algebraic group G. Let $$X_\Sigma be toric variety with . show that when G is reductive set integral maps classifies isomorphism classes (framed) principal G-bundles on This in particular recovers Klyachko’s classification vector bundles, and gives new results for orthog...

Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $sigma$ be a semi-prime operation, different from the identity map on the set of all ideals of $A$. Results of Essan proved that the sets of associated prime ideals of $sigma(I^n)$, which denoted by $Ass(A/sigma(I^n))$, stabilize to $A_{sigma}(I)$. We give some properties of the sets $S^{sigma}_{n}(I)=Ass(A/sigma(I^n))setminus A_{sigma}(I...

For $1$-dimensional Legendrian submanifolds of $1$-jet spaces, we extend the functorality contact homology DG-algebra (DGA) from embedded exact Lagrangian cobordisms, as in \cite{EHK}, to a class immersed cobordisms by considering their lifts conical cobordisms. To cobordism $\Sigma$ $\Lambda_-$ $\Lambda_+$, associate an DGA map, which is diagram $$\alg(\Lambda_+) \stackrel{f}{\rightarrow} \alg...