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<Article>
<Journal>
				<PublisherName>Iranian Mathematical Society (IMS)</PublisherName>
				<JournalTitle>Bulletin of the Iranian Mathematical Society</JournalTitle>
				<Issn>1017-060X</Issn>
				<Volume>37</Volume>
				<Issue>No. 4</Issue>
				<PubDate PubStatus="epublish">
					<Year>2011</Year>
					<Month>12</Month>
					<Day>15</Day>
				</PubDate>
			</Journal>
<ArticleTitle>Generalized sigma-derivation on Banach algebras</ArticleTitle><FirstPage>81</FirstPage>
			<LastPage>94</LastPage>
			<Language>en</Language>
<AuthorList>
<Author>
					<FirstName>A. </FirstName>
					<LastName>Hosseini</LastName>
					<Affiliation></Affiliation>
				</Author>
<Author>
					<FirstName>M. </FirstName>
					<LastName>Hassani</LastName>
					<Affiliation></Affiliation>
				</Author>
<Author>
					<FirstName>A. </FirstName>
					<LastName>Niknam</LastName>
					<Affiliation></Affiliation>
				</Author>
</AuthorList>
			<History>
				<PubDate PubStatus="received">
					<Year>2010</Year>
					<Month>02</Month>
					<Day>28</Day>
				</PubDate>
			</History>
		<Abstract><![CDATA[Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning generalized $sigma$-derivations, we prove that if $mathcal{A}$ is unital and if $delta:mathcal{A} rightarrow mathcal{A}$ is a generalized $sigma$-derivation and there exists an element $a in mathcal{A}$ such that emph{d(a)} is invertible, then $delta$ is continuous if and only if emph{d} is continuous. We also show that if $mathcal{M}$ is unital, has no zero divisor and $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation such that $d(textbf{1}) neq 0$, then $ker(delta)$ is a bi-ideal of $mathcal{A}$ and $ker(delta) = ker(sigma) = ker(d)$, where textbf{1} denotes the unit element of $mathcal{A}$.]]></Abstract>
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			<Param Name="value">Derivation</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">$sigma$-derivation</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">$(sigma</Param>
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			<Object Type="keyword">
			<Param Name="value">d)$-derivation</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">$sigma$-algebraic map</Param>
			</Object>
		</ObjectList>
</Article>
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