2010/11/18 by Martínez, Pascual Jara, Javier López Peña, Peña, Javier López +2
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1011.4243
openalex publication_date 2010/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a semisimple ring. A pair (A,C) is called almost-Koszul if A is a connected graded R-ring and C is a compatible connected graded R-coring. To an almost-Koszul pair one associates three chain complexes and three cochain complexes such that one of them is exact if and only if the others are so. In this situation (A,C) is said to be Koszul. One proves that a connected R-ring A is Koszul if and only if there is a connected R-coring C such that (A,C) is Koszul. This result allows us to investigate the Hochschild (co)homology of Koszul rings. We apply our method to show that the twisted tensor product of two Koszul rings is Koszul. More examples and applications of Koszul pairs, including a generalization of Fröberg Theorem, are discussed in the last part of the paper.