Monic modules and semi-Gorenstein-projective modules

The category gp ( Λ ) of Gorenstein-projective modules over tensor algebra = A ⊗ k B can be described as the monomorphism mon , . In particular, Λ-modules are monic. this paper, we find similar relation between semi-Gorenstein-projective and -modules, via monic modules, namely, ⊥ ∩ Using this, it is proved that if weakly Gorenstein, then Gorenstein only each monic; Q with a finite acyclic quiver, Gorenstein. However, itself does not answer question whether there exist double which recent discovered examples -modules torsionless, positively question, by explicitly constructing class T 2 one parameter such they monic, hence torsionless. corresponding results obtained also for triangular matrix algebras given bimodules