Generalized injectivity
We study whether the projective and injective properties of left -modules can be implied to the special kind of left -modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.
We prove that the Krull-Gabriel dimension of the category of modules over any 1-domestic non-degenerate string algebra is 3.
We prove that an associated graded algebra of a finite dimensional algebra is (= selfinjective) if and only if is and Loewy coincident. Here is said to be Loewy coincident if, for every primitive idempotent , the upper Loewy series and the lower Loewy series of and coincide. -3 algebras are an important generalization of algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra , the associated graded algebra...