Abstract Regarding the question of how idempotent elements affect reversible property rings, we study a version reversibility depending on idempotents. In this perspective, introduce right (resp., left )

The family of rings the form
 \frac{\mathbb{Z}_{4}\left \langle x,y \right \rangle}{\left x^2-a,y^2-b,yx-xy-2(c+dx+ey+fxy) \rangle}
 is investigated which contains generalized Hamilton quaternions over $\Z_4$. These are local order 256. This has 256 contained in 88 distinct isomorphism classes. Of non-isomorphic rings, 10 minimal reversible nonsymmetric and 21 abelian reflexive nonsem...

In this paper, we show that one can construct a \begin{document}$ G $\end{document}-code from group rings is reversible. Specifically, given with subgroup of order half the ambient an element its own inverse outside subgroup, give ordering elements for which id="M4">\begin{document}$ $\end{document}</tex-...

In this paper, we give a new method for constructing LCD codes. We employ group rings and well known map that sends ring elements to subring of the n×n matrices obtain Our construction guarantees our codes are also codes, namely, ideals in ring. show with certain condition on element v, one can construct non-trivial Moreover, by adding more constraints reversible. present many examples binary w...