Exact contexts, noncommutative tensor products, and universal localizations
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- by Hongxing Chen and Changchang Xi PDF
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Abstract:
Exact contexts and their noncommutative tensor products are introduced which generalize the notions of Milnor squares and usual tensor products over commutative rings, respectively. Exact contexts are characterized by rigid morphisms which exist abundantly, while noncommutative tensor products not only capture some useful constructions in ring theory (such as coproducts of rings and trivially twisted extensions) but also provide a new method to construct universal localizations with rich homological and structural information. Moreover, sufficient and necessary conditions in terms of the data of exact contexts are presented to ensure that the universal localizations constructed are homological ring epimorphisms.References
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Additional Information
- Hongxing Chen
- Affiliation: School of Mathematical Sciences, Capital Normal University, 100048 Beijing, People’s Republic of China
- MR Author ID: 888626
- Email: chx19830818@163.com
- Changchang Xi
- Affiliation: School of Mathematical Sciences, Capital Normal University, 100048 Beijing, People’s Republic of China; and School of Mathematics and Information Science, Henan Normal University, 453007 Xinxiang, Henan, People’s Republic of China
- Email: xicc@cnu.edu.cn
- Received by editor(s): November 25, 2016
- Received by editor(s) in revised form: August 4, 2017, and November 8, 2017
- Published electronically: November 5, 2018
- Additional Notes: The research of Hongxing Chen was partially supported by the Natural Science Foundation (11401397) and Beijing Nova Program (Z181100006218010).
The research work of corresponding author Changchang Xi was partially supported by the Natural Science Foundation (11331006).
Parts of this manuscript were revised during a visit of both authors to the University of Stuttgart in May, 2013. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 3647-3672
- MSC (2010): Primary 18E30, 16E35, 13B30, 16G10; Secondary 16S10, 13D09, 16S10
- DOI: https://doi.org/10.1090/tran/7615
- MathSciNet review: 3896125