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- Title
Group-like small cancellation theory for rings.
- Authors
Atkarskaya, A.; Kanel-Belov, A.; Plotkin, E.; Rips, E.
- Abstract
In this paper, we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding defining relations. We show that the obtained ring is non-trivial. Moreover, we show that this ring enjoys a global filtration that agrees with relations, find a basis of the ring as a linear space and establish the corresponding structure theorems. We also provide a revision of a concept of Gröbner basis for our rings and establish a greedy algorithm for the Ideal Membership Problem.
- Subjects
RING theory; GROUP algebras; ASSOCIATIVE algebras; FREE groups; VECTOR spaces
- Publication
International Journal of Algebra & Computation, 2023, Vol 33, Issue 7, p1269
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196723500522