Algebras Stratified for all Linear Orders

Abstract

In this paper we describe several characterizations of basic finite-dimensional $\Bbbk$ -algebras A stratified for all linear orders, and classify their graded algebras as tensor algebras satisfying some extra property. We also discuss whether for a given linear order $\preccurlyeq$ , $\mathcal{F} (_{\preccurlyeq} \Delta)$ , the category of A-modules with $_{\preccurlyeq} \Delta$ -filtrations, is closed under cokernels of monomorphisms, and classify quasi-hereditary algebras satisfying this property.