A decomposition theorem for comodules
A duality result for almost split sequences
Over an artinian hereditary ring R, we discuss how the existence of almost split sequences starting at the indecomposable non-injective preprojective right R-modules is related to the existence of almost split sequences ending at the indecomposable non-projective preinjective left R-modules. This answers a question raised by Simson in [27] in connection with pure semisimple rings.
A functional equation for quadratic forms.
A general concept of the pseudoprojective module
A Homological Finiteness Criterion.
A noncommutative generalization of Auslander's last theorem.
A note on -cofinitely supplemented modules.
A note on flat modules
A note on free direct summands.
A note on perfect modules over crossed products
A note on test modules
A Reduction Theorem for the Primitivity of Tensor Products.
A remark on -torsion-free modules
A Remark on Projective Dimension of Fiat Modules.
A Remark on Pure Ideals and Projective Modules.
Almost split sequences for non-regular modules
Let A be an Artin algebra and let be an almost split sequence of A-modules with the indecomposable. Suppose that X has a projective predecessor and Z has an injective successor in the Auslander-Reiten quiver of A. Then r ≤ 4, and r = 4 implies that one of the is projective-injective. Moreover, if is a source map with the indecomposable and X on an oriented cycle in , then t ≤ 4 and at most three of the are not projective. The dual statement for a sink map holds. Finally, if an arrow...
Almost Split Sequences over p-adic Rings.
Almost-flat modules
We present general properties for almost-flat modules and we prove that a self-small right module is almost flat as a left module over its endomorphism ring if and only if the class of -static modules is closed under the kernels.
Automorphism liftable modules
We introduce the notion of an automorphism liftable module and give a characterization to it. We prove that category equivalence preserves automorphism liftable. Furthermore, we characterize semisimple rings, perfect rings, hereditary rings and quasi-Frobenius rings by properties of automorphism liftable modules. Also, we study automorphism liftable modules with summand sum property (SSP) and summand intersection property (SIP).