2021/05/10 by Robert J. MacG. Dawson, Dawson, Robert, Grant Molnar +1
Mathematics · #13F25 #16W60 (Secondary) #40C99 (Primary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2105.04592
openalex publication_date 2021/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A summation is a shift-invariant \rm R-module homomorphism from a submodule of \rm R[[σ]] to \rm R or another ring. [11] formalized a method for extending a summation to a larger domain by telescoping. In this paper, we revisit telescoping, we study multiplicative closures of summations (such as the usual summation on convergent series) that are not themselves multiplicatively closed, and we study rational extensions as a generalization of telescoping.