Quasi-duality for the rings of generalized power series. (English) Zbl 0948.16005
Authors’ abstract: Let \(A\), \(B\) be associative rings with identity, and \((S,\leq)\) a strictly totally ordered commutative monoid which is also Artinian. For any bimodule \(_AM_B\), we construct a bimodule \(_{A[[S]]}M[S]_{B[[S]]}\) and prove that \(_AM_B\) defines a quasi-duality if and only if the bimodule \(_{A[[S]]}M[S]_{B[[S]]}\) defines a quasi-duality. As a corollary, it is shown that if a ring \(A\) has a quasi-duality then the ring \(A[[S]]\) of generalized power series over \(A\) has a quasi-duality.
Reviewer: Xue Weimin (Fujian)
MSC:
| 16D90 | Module categories in associative algebras |
| 16D20 | Bimodules in associative algebras |
| 16W60 | Valuations, completions, formal power series and related constructions (associative rings and algebras) |
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