C. Menini and A. Orsatti [Rend. Sem. Mat. Univ. Padova 82 (1989), 203--231 (1990); MR1049594 (91h:16026)] introduced ∗-modules in order to characterize equivalences between certain full subcategories of module categories over two rings. If one restricts the study to the case of finite-dimensional algebras over a field k, it was shown by G. D'Este and the reviewer [Rend. Sem. Mat. Univ. Padova 83 (1990), 77--80; MR1066430 (91i:16027)] that faithful ∗-modules are tilting modules in the sense of the reviewer and C. M. Ringel [Trans. Amer. Math. Soc. 274 (1982), no. 2, 399--443; MR0675063 (84d:16027)]. The paper under review now generalizes this characterization to arbitrary rings using the natural generalizations for tilting modules in this case.
Tilting modules and $*$-modules
COLPI, RICCARDO
1993
Abstract
C. Menini and A. Orsatti [Rend. Sem. Mat. Univ. Padova 82 (1989), 203--231 (1990); MR1049594 (91h:16026)] introduced ∗-modules in order to characterize equivalences between certain full subcategories of module categories over two rings. If one restricts the study to the case of finite-dimensional algebras over a field k, it was shown by G. D'Este and the reviewer [Rend. Sem. Mat. Univ. Padova 83 (1990), 77--80; MR1066430 (91i:16027)] that faithful ∗-modules are tilting modules in the sense of the reviewer and C. M. Ringel [Trans. Amer. Math. Soc. 274 (1982), no. 2, 399--443; MR0675063 (84d:16027)]. The paper under review now generalizes this characterization to arbitrary rings using the natural generalizations for tilting modules in this case.
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