Projective indecomposable modules and quivers for monoid algebras. Issue 12 (2nd December 2018)

• Record Type: Journal Article
• Authors: Margolis, Stuart; Steinberg, Benjamin
• Is Part Of: Communications in algebra. Volume 46:Issue 12(2018)
• Page Start: 5116
• Page End: 5135
• Publication Date: 2018-12-02
• Subjects: Fountain monoid -- Monoid algebra -- projective modules -- quivers; 20M25 -- 16G10 -- 05E99; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1448841
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: We give a construction of the projective indecomposable modules and a description of the quiver for a large class of monoid algebras including the algebra of any finite monoid whose principal right ideals have at most one idempotent generator. Our results include essentially all families of finite monoids for which this has been done previously, for example, left regular bands, 𝒥 -trivial and ℛ -trivial monoids and left regular bands of groups.