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Paper Title: Generalised Inner Derivations
Authors Name: Dr. K.L. Kaushik
Unique Id: IJSDR2008026
Published In: Volume 5 Issue 8, August-2020
Abstract: . Let A be any ring and f be a generalised inner derivation of A. For any x,y ∈ A, we have f(xy) = f(x)y + xha(y) for fixed element a ∈ A. In this paper, it is shown that (i) If r f(x) = 0 for every r,x ∈ A, A = Prime ring. Then either r = 0 or ha = 0 (ii) f(xyz) = f(xy)z + xf(yz) − xf(y)z ∀ x,y,z ∈ A (iii) f(aba) = f(a)ba ∀ b ∈ A. We proved Posner [4] Lemma 1 P.1093, Bresar [1] Obs.1, Remark 3, P.90, Havala [2] Def. P1147 as Corollaries along with other results.
Keywords: . Generalised inner derivation, Prime ring, Ideal, Ring with unity, Ring without zero divisors.
Cite Article: "Generalised Inner Derivations", International Journal of Science & Engineering Development Research (www.ijsdr.org), ISSN:2455-2631, Vol.5, Issue 8, page no.234 - 236, August-2020, Available :http://www.ijsdr.org/papers/IJSDR2008026.pdf
Downloads: 00060116
Publication Details: Published Paper ID: IJSDR2008026
Registration ID:192338
Published In: Volume 5 Issue 8, August-2020
DOI (Digital Object Identifier):
Page No: 234 - 236
Publisher: IJSDR | www.ijsdr.org
ISSN Number: 2455-2631

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