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- Title
Classification of Rings Associated with the Genus of Clean Graphs.
- Authors
Ramanathan, V.; Selvaraj, C.; Altaf, Aaqib; Pirzada, S.
- Abstract
Let R be a ring (not necessarily commutative) with identity 1 and let CL (R) be its clean graph. In this paper, we investigate the genus number of the compact Riemann surface in which CL (R) can be embedded and explicitly determine all commutative rings R (up to isomorphism) such that CL (R) has genus at most two. It is shown that for any Artinian ring R , CL (R) is a projective graph if and only if R is isomorphic to F 4. Furthermore, we determine all isomorphism classes of commutative rings whose clean graphs have crosscap two.
- Subjects
ISOMORPHISM (Mathematics); PLANAR graphs; CLASSIFICATION; RIEMANN surfaces
- Publication
Algebra Colloquium, 2024, Vol 31, Issue 3, p451
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386724000348