New Types of Permuting n-Derivations with Their Applications on Associative Rings

Abstract

In this article, we introduce new generators of a permuting n-derivations to improve and increase the action of usual derivation. We produce a permuting n-generalized semiderivation, a permuting n-semigeneralized semiderivation, a permuting n-antisemigeneralized semiderivation and a permuting skew n-antisemigeneralized semiderivation of non-empty rings with their applications. Actually, we study the behaviour of those types and present their results of semiprime ring R. Examples of various results have also been included. That is, many of the branches of science such as business, engineering and quantum physics, which used a derivation, have the opportunity to invest them in solving their problems.

$(σ, τ)$-Derivations of Group Algebras

“…Differentiable manifolds, operator algebras, C * -algebras, representation theory of Lie groups are continued to be studied using derivations [12]. For more applications of derivations, we refer the reader to [3]. Derivations on rings and algebras help in the study of their structure.…”