TY - JOUR ID - 378 TI - On module extension Banach algebras JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Medghalchi, A. AU - Pourmahmood-Aghababa, H. AD - Y1 - 2011 PY - 2011 VL - 37 IS - No. 4 SP - 171 EP - 183 KW - Module extension Banach algebras KW - Biflatness KW - biprojectivity KW - Weak amenability KW - Automatic continuity DO - N2 - 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 ${mathcal{S}}=Aoplus A$. UR - http://bims.iranjournals.ir/article_378.html L1 - http://bims.iranjournals.ir/article_378_751f25bfc812837d15a214e91d2fd439.pdf ER -