In this paper we carry out a systematic study of modules over a
formal triangular matrix ring T=[
]. Using the altenative description of right
T-modules as triples (X,Y)f with X ∈ Mod−A,Y ∈ Mod −B and
f:Y⊗B M→ X in Mod−A, we shall characterize
respectively uniform, hollow, finitely embedded, projective,
generator or progenerator modules over T. For projective modules
an explicit method for constructing a dual basis is described.
Also necessary and sufficient conditions are found for a
T-module to admit a projective cover. When the conditions are
fulfilled we give an explicit method for constructing a projective
cover.
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