Open AccessGeneralised Inner Derivations in Semi Prime Rings
Author(s) -
K. L Kaushik
Publication year - 2020
Publication title -
international journal of innovative science and research technology
Language(s) - English
Resource type - Journals
ISSN - 2456-2165
DOI - 10.38124/ijisrt20aug277
Subject(s) - prime (order theory) , lemma (botany) , mathematics , ring (chemistry) , combinatorics , element (criminal law) , prime ring , chemistry , ecology , poaceae , organic chemistry , political science , law , biology
Let A be any ring and f(xy) = f(x)y+xha(y), where f be any generalised inner derivation(G.I.D ) a be the fixed element of A. In this paper, it is shown that (i) ha must necessarily be a derivation for semi prime ring A. (ii) ∃ no generalized inner derivations f : A → A such that f(x ◦ y) = x ◦ y or f(x ◦ y) + x ◦ y = 0 ∀ x,y ∈ A, We have proved Havala [2] def. p.1147, Herstein [3] Lemma 3.1 p. 1106 as corollaries, along with other results.