2007/07/08 by Kohji Yanagawa, Yanagawa, Kohji
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.0707.1134
openalex publication_date 2007/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a Koszul algebra, and mod A the category of finitely generated graded left A-modules. The "linearity defect" ldA(M) of M ∈ mod A is an invariant defined by Herzog and Iyengar. An exterior algebra E is a Koszul algebra which is the Koszul dual S^! of a polynomial ring S. Eisenbud et al. showed that ldE(M) < ∞ for all M ∈ mod E. Improving their result, we show the following (and many other facts): (*) If A is a Koszul complete intersection, then regA^! (M) < ∞ and ldA^! (M) < ∞ for all M ∈ mod A^!. (**) There is a uniform bound of ld(J), where J is a graded ideal of E.