2009/12/20 by Abasalt Bodaghi, Bodaghi, Abasalt, Massoud Amini +1 · 1 citation
Mathematics · #46H25 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Rings, Modules, and Algebras #math.FA #msc:46H25
paper · pdf · doi:10.48550/arxiv.0912.4005
12 pages
arxiv created 2009/12/20 · openalex publication_date 2009/12/20 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we define module biprojctivity and module biflatness for a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and find their relation to classical biprojectivity and biflatness. As a typical example, We show that for an inverse semigroup S with an upward directed set of idempotents E, the semigroup algebra ℓ 1(S), as an ℓ 1(E)-module, is module biprojective if and only if an appropriate group homomorphic image of S is finite. Also we show that ℓ 1(S) is module biflat if and only if S is amenable.