Title of article :
Boolean Rings Based on Multirings
Author/Authors :
Ameri, R School of Mathematics - Statistics and Computer Sciences - University of Tehran - Tehran, Islamic Repupblic of Iran , Hamidi, M Department of Mathematics - Faculty of Mathematics - University of Payam-e- Noor - Tehran, Islamic Republic of Iran , Tavakoli, A.A Department of Mathematics - Faculty of Mathematics - University of Payam-e- Noor - Tehran, Islamic Republic of Iran
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 :
Boolean ring , Multigroup , Multiring , Fundamental relation
Journal title :
Journal of Sciences Islamic Republic of Iran
