Document Type : Original Paper

Authors

• Ebrahim Nasrabadi ¹
• Mohammad Ramezanpour ²
• Asadollah Aasaraai ³

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

Abstract

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 .

Keywords

• Inverse semigroup
• Triangular Banach algebra
• First module cohomology group
• Weak module amenability, ("n)" -weak module amenability