2007/12/07 by Lars Hellström, Hellström, Lars
Computer Science · Mathematics · #03C05 (Secondary) #16S15 (Primary) #16W60 #16Z05 #18D50 #22A05 #FOS: Mathematics #Logic, programming, and type systems #Numerical Methods and Algorithms #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.RA #msc:03C05 #msc:16S15 #msc:16W60 #msc:16Z05 #msc:18D50 #msc:22A05
paper · pdf · doi:10.48550/arxiv.0712.1142
74 pages. Includes index
arxiv created 2007/12/07 · openalex publication_date 2007/12/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper gives a generic form of the diamond lemma, which includes support for additive and topological structures of the base set, and which does not require any further structure (e.g. an associative multiplication operation) to be present. This result is intended to be used as the core of diamond lemmas for particular algebraic structures, taking care of all the common technicalities. With this generic diamond lemma, the main steps needed to prove a specialised diamond lemma is to define the reduction maps and analyse the structure of critical ambiguities. The abstract machinery is backed up with concrete suggestions for how one should set things up in order to reproduce traditional results in the general setting. Several instances of the fundamental theorem of Groebner basis theory are derived as corollaries of the main result.