Matlis category equivalences for a ring epimorphism

0524150 - MÚ 2021 RIV NL eng J - Článek v odborném periodiku
Bazzoni, S. - Positselski, Leonid
Matlis category equivalences for a ring epimorphism.
Journal of Pure and Applied Algebra. Roč. 224, č. 10 (2020), č. článku 106398. ISSN 0022-4049. E-ISSN 1873-1376
Institucionální podpora: RVO:67985840
Klíčová slova: associative ring epimorphisms * comodules and contramodules * triangulated recollement
Obor OECD: Pure mathematics
Impakt faktor: 0.831, rok: 2020
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jpaa.2020.106398

Under mild assumptions, we construct the two Matlis additive category equivalences for an associative ring epimorphism u: R->U. Assuming that the ring epimorphism is homological of flat/projective dimension 1, we discuss the abelian categories of u-comodules and u-contramodules and construct the recollement of unbounded derived categories of R-modules, U-modules, and complexes of R-modules with u-co/contramodule cohomology. Further assumptions allow to describe the third category in the recollement as the unbounded derived category of the abelian categories of u-comodules and u-contramodules. For commutative rings, we also prove that any homological epimorphism of projective dimension 1 is flat. Injectivity of the map u is not required.
Trvalý link: http://hdl.handle.net/11104/0308514