Document Type : Original Paper


1 Department of Mathematic, Faculty of Mathematic Science and Statistic‎s, University of Birjand, Birjand, Islamic Republic of Iran

2 School of Mathematics and Computer Science‎, ‎Damghan University‎, ‎Damghan‎, ‎ Islamic Republic of Iran

3 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Islamic Republic of Iran


Let  be a commutative (not necessary unital) inverse semigroup with the set of idempotents  ‎then  is a commutative Banach‎ -module with canonical actions‎. ‎Recently‎, ‎it is shown that the triangular Banach algebra

is -weakly -module amenable‎, ‎provided that  and  is unital or  satisfies condition  for some ‎. ‎In this paper‎, ‎we show that  is -weakly -module amenable‎, ‎without any additional conditions on  and , ‎if  is a certain quotient space of .