University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 32 2 2021 05 01 Boolean Rings Based On Multirings 159 167 81172 10.22059/jsciences.2021.295842.1007481 EN Reza Ameri 1 School of Mathematics, Statistics and Computer Sciences, University of Tehran, Tehran, Islamic Repupblic of Iran 0000-0001-5760-1788 Ali Tavakoli 2 Department of Mathematics, Faculty of Mathematics, University of Payam-e- Noor, Tehran, Islamic Republic of Iran Mohammad Hamidi 2 Department of Mathematics, Faculty of Mathematics, University of Payam-e- Noor, Tehran, Islamic Republic of Iran Journal Article 2020 02 04 The purpose of this paper is to construct Boolean rings from multirings. In this regards, a method to construct a multigroup(multiring) on a given non<strong>-</strong>empty set, are introduced and its properties has been investigated. Also, an equivalence relation on a multiring are introduced and it is extended to an smallest strongly regular  equivalence relation, such that its quotient  space be a commutative Boolean ring with identity. Finally, the transitivity of this relation based on complete parts are   proved. https://jsciences.ut.ac.ir/article_81172_9ff66c3b9bbdd8cf2a12fe692c36711a.pdf