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<!DOCTYPE ArticleSet PUBLIC "-//NLM//DTD PubMed 2.6//EN" "http://www.ncbi.nlm.nih.gov/corehtml/query/static/PubMed.dtd">
<ArticleSet>
<Article>
<Journal>
				<PublisherName>Iranian Mathematical Society (IMS)</PublisherName>
				<JournalTitle>Bulletin of the Iranian Mathematical Society</JournalTitle>
				<Issn>1017-060X</Issn>
				<Volume>38</Volume>
				<Issue>4</Issue>
				<PubDate PubStatus="epublish">
					<Year>2012</Year>
					<Month>12</Month>
					<Day>15</Day>
				</PubDate>
			</Journal>
<ArticleTitle>On generalized left (alpha, beta)-derivations in rings</ArticleTitle><FirstPage>893</FirstPage>
			<LastPage>905</LastPage>
			<Language>en</Language>
<AuthorList>
<Author>
					<FirstName>Mohammad </FirstName>
					<LastName>Ashraf</LastName>
					<Affiliation>Aligarh Muslim University</Affiliation>
				</Author>
<Author>
					<FirstName>Shakir </FirstName>
					<LastName>Ali</LastName>
					<Affiliation>Aligarh Muslim University</Affiliation>
				</Author>
<Author>
					<FirstName>Nadeem ur</FirstName>
					<LastName>Rehman</LastName>
					<Affiliation>Aligarh Muslim University</Affiliation>
				</Author>
<Author>
					<FirstName>Muzibur Rahman</FirstName>
					<LastName>Mozumder</LastName>
					<Affiliation>Aligarh Muslim University</Affiliation>
				</Author>
</AuthorList>
			<History>
				<PubDate PubStatus="received">
					<Year>2010</Year>
					<Month>07</Month>
					<Day>03</Day>
				</PubDate>
			</History>
		<Abstract><![CDATA[Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G : Rlongrightarrow R$ satisfying   $G(u^2)=alpha(u)G(u)+alpha(u)delta(u)$ for all $uin U$ and a Jordan left $(alpha,alpha)$-derivation $delta$; and $U$ has a commutator which is not a left zero divisor, then $G(uv)=alpha(u)G(v)+alpha(v)delta(u)$ for all $u, vin U$. Finally, in the case of prime ring $R$ it is proved that if $G: R longrightarrow R$ is an additive mapping satisfying $G(xy)=alpha(x)G(y)+beta(y)delta(x)$ for all $x,y in R $ and a left $(alpha, beta)$-derivation $delta$ of $R$ such that $G$ also  acts as a homomorphism or as an linebreak anti-homomorphism on a nonzero ideal $I$ of $R$, then either $R$ is commutative or $delta=0$ ~on $R$.]]></Abstract>
		<ObjectList>
			<Object Type="keyword">
			<Param Name="value">Prime ring</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">Lie ideal</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">Jordan left (alpha,beta)-derivation</Param>
			</Object>
		</ObjectList>
</Article>
</ArticleSet>