Document Type : Original Paper


1 1 School of Mathematics, Statistics and Computer Sciences, University of Tehran, Tehran, Islamic Repupblic of Iran

2 2 Department of Mathematics, Faculty of Mathematics, University of Payam-e- Noor, Tehran, Islamic Republic of Iran


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-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.