TY - JOUR ID - 94188 TI - Distributive lattices and some related topologies in comparison with zero-divisor graphs JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Bagheri, Saeid AU - Koohi Kerahroodi, mahtab AD - Department of Mathematics, Malayer University, P.O.Box: 65719-95863, Malayer, Iran. Y1 - 2021 PY - 2021 VL - 14 IS - 1 SP - 223 EP - 244 KW - Distributive lattice KW - Goldie dimension KW - compressed zero-divisor graph KW - domination number DO - 10.29252/cgasa.14.1.223 N2 - In this paper,for a distributive lattice $\mathcal L$, we study and compare some lattice theoretic features of $\mathcal L$ and topological properties of the Stone spaces ${\rm Spec}(\mathcal L)$ and ${\rm Max}(\mathcal L)$ with the corresponding graph theoretical aspects of the zero-divisor graph $\Gamma(\mathcal L)$.Among other things,we show that the Goldie dimension of $\mathcal L$ is equal to the cellularity of the topological space ${\rm Spec}(\mathcal L)$ which is also equal to the clique number of the zero-divisor graph $\Gamma(\mathcal L)$. Moreover, the domination number of $\Gamma(\mathcal L)$ will be compared with the density and the weight of the topological space ${\rm Spec}(\mathcal L)$. For a $0$-distributive lattice $\mathcal L$, we investigate the compressed subgraph $\Gamma_E(\mathcal L)$ of the zero-divisor graph $\Gamma(\mathcal L)$ and determine some properties of this subgraph in terms of some lattice theoretic objects such as associated prime ideals of $\mathcal L$. UR - https://cgasa.sbu.ac.ir/article_94188.html L1 - https://cgasa.sbu.ac.ir/article_94188_8886cc33fcfa95bf3e8a98c714546517.pdf ER -