On the problem of the finiteness of the compressed zero divisor graphs of Artinian rings

Autor:	Kadu, Ganesh S.
Rok vydání:	2020
Předmět:	Mathematics - Combinatorics Mathematics - Rings and Algebras Primary 13A70 05E40 Secondary 05C69 13E39
Druh dokumentu:	Working Paper
Popis:	Let R be an Artinian ring and G be the compressed zero-divisor graph associated to R. The question of when the clique number of compressed zero-divisor graphs is finite was raised by J. Coykendall, S. Sather-Wagstaff, L. Sheppardson, and S. Spiroff, in their survey paper entitled On Zero-divisor Graphs. They proved that if length of R is at most four then the clique number is finite. In the length six case they gave an example of a ring where the clique is infinite. In this paper we show that when length of ring is five then the clique number of compressed zero-divisor graph is finite. Comment: 16 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.06924 Zobrazit plný text záznamu View this record from Arxiv