It is shown that the Baer–Kaplansky Theorem can be extended to all abelian groups provided rings of endomorphisms are replaced by trusses corresponding heaps. That is, every group determined up isomorphism its endomorphism truss and between two associated some [Formula: see text] induced an element from text]. This correspondence then modules over a ring considering heaps modules. proved heap m...

A right Johns ring is a Noetherian in which every ideal annihilator. It known that RR the Jacobson radical J(R)J(R) of nilpotent and Soc(R)(R) an essential RR. Moreover, Kasch, is, simple RR-module can be embedded For M∈RM∈R-Mod we use concept MM-annihilator define module (resp. quasi-Johns) as MM such submodule MM-annihilator. called quasi-Johns if any set submodules satisfies ascending chain ...

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 approximately quasi in...

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...

in this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. in particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over noetherian rings are proved. moreover, w...