%0 Journal Article %T On module extension Banach algebras %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Medghalchi, A. %A Pourmahmood-Aghababa, H. %D 2011 %\ 12/15/2011 %V 37 %N No. 4 %P 171-183 %! On module extension Banach algebras %K Module extension Banach algebras %K Biflatness %K biprojectivity %K Weak amenability %K Automatic continuity %R %X Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. Then ${mathcal{S}}=A oplus X$, the $l^1$-direct sum of $A$ and $X$ becomes a module extension Banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we investigate biflatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on ${mathcal{S}}=Aoplus A$. %U http://bims.iranjournals.ir/article_378_751f25bfc812837d15a214e91d2fd439.pdf