Payrovi, ShiroyehBabaei, SakinehSevim, Esra Sengelen2024-07-182024-07-1820191370-14442034-1970https://doi.org/10.36045/bbms/1568685656https://hdl.handle.net/11411/8187Let R be a commutative ring. In this paper, we introduce and study the compressed essential graph of R, EG(E)(R). The compressed essential graph of R is a graph whose vertices are equivalence classes of non-zero zero-divisors of R and two distinct vertices [x] and [y] are adjacent if and only if ann(xy) is an essential ideal of R. It is shown if R is reduced, then EG(E)(R) = Gamma(E)(R), where Gamma(E)(R) denotes the compressed zero-divisor graph of R. Furthermore, for a non-reduced Noetherian ring R with 3 < vertical bar EG(E)(R)vertical bar < infinity, it is shown that EG(E)(R) = Gamma(E)(R) if and only if (i) Nil(R) = ann(Z(R)). (ii) Every non-zero element of Nil(R) is irreducible in Z(R).eninfo:eu-repo/semantics/closedAccessEssential GraphZero Divisor GraphCompressed Zero-Divisor Graph2-Absorbing İdealZero-Divisor GraphArticle2-s2.0-8507413610710.36045/bbms/15686856564293Q342126Q4WOS:000486383700007