University of Guilan Journal of Algebra and Related Topics 2345-3931 10 2 2022 12 01 Semisimple lattices with respect to filter theory 131 143 6006 10.22124/jart.2022.21065.1342 EN S. Ebrahimi Atani Department of Mathematics, University of Guilan, Rasht, Iran 0009-0001-2215-9640 M. Khoramdel Department of Mathematics, University of Guilan, Rasht, Iran S. Dolati Pish Hesari Department of Mathematics, University of Guilan, Rasht, Iran M. Nikmard Rostam Alipour Department of Mathematics, University of Guilan, Rasht, Iran Journal Article 2021 11 11 Since the theory of filters plays an important role in the theory of lattices, in this paper, we will make an intensive study of the notions of semisimple lattices and the socle of lattices based on their filters. The bulk of this paper is devoted to stating and proving analogues to several well-known theorems in the theory of the rings. It is shown that, if $L$ is a semisimple distributive lattice, then $L$ is finite. Also, an application of the results of this paper is given. It is shown that if $R$ is a right distributive ring, then the lattice of right ideals of $R$ is semisimple iff  $R$ is a semisimple ring. https://jart.guilan.ac.ir/article_6006_00e587f67ee2b48058f2e33ef78730cd.pdf