Duality Theorem of Character Modules for Rings with Minimum Condition.
On algebras of which every indecomposable representation has an irreducible one as the top or the bottom Loewy constituent.
On Rings for which Every Indecomposable Right Module has a Unique Maximal Submodule.
Double Centralizers and Dominant Dimensions.
On Splitting of Module Categories.
Localization and Artinian Quotient Rings.
Loewy coincident algebra and -3 associated graded algebra
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...
Character modules, submodules of a free module, and quasi-Frobenius rings.
On injective modules.
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