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	\emph{ \textbf{: ABSTRACT } }
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	\emph{  	 
		Given a morphism T from a Banach algebra B to a commutative Banach algebra A, a nultiplication is defined on the Cartesian product space $ A\timesB$ perturrbing the coordinatewise product resulting in a new Banach algebra  $ A\timesB$  . The Arnes regularity as well as amenability (together with its various avatars) of  $ A\timesB$ are shown to be stable with respect to T.\\
		\textbf{Key words and phrases: Arnes regularity, amenability, approximate amenability, cyclic amenability, character amenability.}    }
	
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