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IPM
30
YEARS OLD

“School of Mathematics”

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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