We investigate some properties of approximately quasi inner generalized dynamics and quasi approximately inner generalized derivations on modules. In particular, we prove that if A is a C*-algebra, is the generator of a generalized dynamics on an A-bimodule M satisfying and there exist two sequences of self adjoint elements in A such that for all in a core for , , then is approx...

The main goal of this paper is to introduce a new class in the category modules. It called quasi-invertibility monoform (briefly QI-monoform) This modules generalization Various properties and another characterization QI-monoform are investigated. So, we prove that an R-module M if only for each non-zero homomorphism f:M E(M), kernel not quasi-invertible submodule M. Moreover, cases under which...

Trinion and Quaternion numbers are one of the hypercomplex which is an extensions complex number. From numbers, a bimodule can be formed ordered pair Quaternion. Furthermore, number, their into Formal Triangle Matrix. The Matrix better known as Upper Since number rings, then called Triangular Ring. purpose this study to construct Armendariz Ring using obtained results will show that Rings -Skew...

 The class of ads modules with the SIP (briefly‎, ‎$SA$-modules) is studied‎. ‎Various conditions for a module to be $SA$-module are given‎. ‎It is proved that for a quasi-continuous module $M$‎, ‎$M$ is a UC-module if and only if $M$ is an $SA$-module‎. ‎Also‎, ‎it is proved that the direct sum of two $SA$-modules as $R$-modules is an $SA$-module when $R$ is the sum of the annihilators of thes...

A theory of quasi modules at infinity for (weak) quantum vertex algebras including vertex algebras was previously developed in [Li6]. In this current paper, we develop this theory of quasi modules at infinity for vertex algebras further. Among the main results, we obtain a commutator formula for general quasi modules at infinity and we establish a category equivalence between the category of qu...

In this paper we show that a direct decomposition of modules M N, with N homologically independent to the inJective hull of H, is a CS-module if and only if N is injective relative to H and both of M and N are CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for q...