On additivity of derivations

Let $R$ be a ring and $M$ be an $R$-bimodule. A mapping $d:R\rightarrow M$ (not necessarily additive) is called multiplicative derivation of $R$ if $d(xy)=d(x)y+xd(y)$ for all $x,y\in R.$ In this paper, we intend to establish the additivity of $d$ under some suitable restrictions. Moreover, we intro...

Full description

Bibliographic Details
Main Authors:	G.S. Sandhu, D. Kumar
Format:	Article
Language:	English
Published:	Vasyl Stefanyk Precarpathian National University 2019-12-01
Series:	Karpatsʹkì Matematičnì Publìkacìï
Subjects:	derivation multiplicative derivation multiplicative semi-derivation additivity peirce decomposition
Online Access:	https://journals.pnu.edu.ua/index.php/cmp/article/view/2123

id	doaj-41d60039e1f340c8b1f82a013ae31fe4
record_format	Article
spelling	doaj-41d60039e1f340c8b1f82a013ae31fe42020-11-25T03:20:58ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102019-12-0111245346210.15330/cmp.11.2.453-4622123On additivity of derivationsG.S. Sandhu0D. Kumar1Patel Memorial National College Rajpura, 140401, Punjab, IndiaPunjabi University, 147002, Patiala, IndiaLet $R$ be a ring and $M$ be an $R$-bimodule. A mapping $d:R\rightarrow M$ (not necessarily additive) is called multiplicative derivation of $R$ if $d(xy)=d(x)y+xd(y)$ for all $x,y\in R.$ In this paper, we intend to establish the additivity of $d$ under some suitable restrictions. Moreover, we introduce multiplicative semi-derivations of rings and discuss their additivity.https://journals.pnu.edu.ua/index.php/cmp/article/view/2123derivationmultiplicative derivationmultiplicative semi-derivationadditivitypeirce decomposition
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	G.S. Sandhu D. Kumar
spellingShingle	G.S. Sandhu D. Kumar On additivity of derivations Karpatsʹkì Matematičnì Publìkacìï derivation multiplicative derivation multiplicative semi-derivation additivity peirce decomposition
author_facet	G.S. Sandhu D. Kumar
author_sort	G.S. Sandhu
title	On additivity of derivations
title_short	On additivity of derivations
title_full	On additivity of derivations
title_fullStr	On additivity of derivations
title_full_unstemmed	On additivity of derivations
title_sort	on additivity of derivations
publisher	Vasyl Stefanyk Precarpathian National University
series	Karpatsʹkì Matematičnì Publìkacìï
issn	2075-9827 2313-0210
publishDate	2019-12-01
description	Let $R$ be a ring and $M$ be an $R$-bimodule. A mapping $d:R\rightarrow M$ (not necessarily additive) is called multiplicative derivation of $R$ if $d(xy)=d(x)y+xd(y)$ for all $x,y\in R.$ In this paper, we intend to establish the additivity of $d$ under some suitable restrictions. Moreover, we introduce multiplicative semi-derivations of rings and discuss their additivity.
topic	derivation multiplicative derivation multiplicative semi-derivation additivity peirce decomposition
url	https://journals.pnu.edu.ua/index.php/cmp/article/view/2123
work_keys_str_mv	AT gssandhu onadditivityofderivations AT dkumar onadditivityofderivations
_version_	1724615613131784192

On additivity of derivations

Similar Items