University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 32 4 2021 12 01 (2n+1)-Weak Module Amenability of Triangular Banach Algebras on Inverse Semigroup Algebras 341 347 80609 10.22059/jsciences.2021.295337.1007478 EN Ebrahim Nasrabadi Department of Mathematic, Faculty of Mathematic Science and Statistic‎s, University of Birjand, Birjand, Islamic Republic of Iran Mohammad Ramezanpour School of Mathematics and Computer Science‎, ‎Damghan University‎, ‎Damghan‎, ‎ Islamic Republic of Iran Asadollah Aasaraai Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Islamic Republic of Iran Journal Article 2020 01 05 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<br />‎<br />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 . Inverse semigroup Triangular Banach algebra First module cohomology group Weak module amenability, ("n)" -weak module amenability https://jsciences.ut.ac.ir/article_80609_22fcadaa3ef1f9f7a311dce86952a300.pdf