Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group-like small cancellation theory for rings   In the present 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 vector space and establish the corresponding structure
theorems. We also provide a revision of a concept of Gr\"{o}bner basis for our
rings and establish a greedy algorithm for the Ideal Membership Problem.

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The categories of this paper are: chem-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio