Abstract
The theory of adjoint functors has been used by Morita to develop a theory of Frobenius and quasi-Frobenius extensions subsuming the work of Kasch, Müller, Nakayama, and others. We use adjoint functors to define a pairing of the two rings and develop a theory of relative projective and injective modules for pairings generalizing that of Hochschild for extensions. The main purpose of this paper is to define “strongly separable pairings” generalizing strongly separable (i.e. finitely generated projective separable) algebras. We show that such pairings have very close connections to category equivalences, so that it is natural to investigate those properties shared by two rings which admit a strongly separable pairing. We show that most “categorical” properties are so shared.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
