@article { author = {Ameri, Reza and Tavakoli, Ali and Hamidi, Mohammad}, title = {Boolean Rings Based On Multirings}, journal = {Journal of Sciences, Islamic Republic of Iran}, volume = {32}, number = {2}, pages = {159-167}, year = {2021}, publisher = {University of Tehran}, issn = {1016-1104}, eissn = {2345-6914}, doi = {10.22059/jsciences.2021.295842.1007481}, abstract = {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.}, keywords = {Multigroup,multiring,fundamental relation,Boolean ring}, url = {https://jsciences.ut.ac.ir/article_81172.html}, eprint = {https://jsciences.ut.ac.ir/article_81172_9ff66c3b9bbdd8cf2a12fe692c36711a.pdf} }