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IPM
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“School of Mathematics”

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Paper   IPM / M / 109
School of Mathematics
  Title:   Study of modules over formal triangular matrix rings
  Author(s): 
1.  A. Haghany
2.  K. Varadarajan
  Status:   Published
  Journal: J. Pure Appl. Algebra
  Vol.:  147
  Year:  2000
  Pages:   41-58
  Supported by:  IPM
  Abstract:
In this paper we carry out a systematic study of modules over a formal triangular matrix ring T=[
A
0
M
B
]. Using the altenative description of right T-modules as triples (X,Y)f with XModA,YModB and f:YB MX in ModA, 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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