journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2638 Soft rings based on soft binary operations Jemberie Yohannes Taye Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia Belayneh Berhanu Bekele Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia Wale Zelalem Teshome Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia Addis Gezahagne Mulat Department of Mathematics, University of Gondar, Gondar, Ethiopia Fufa Samuel Asefa Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia Sharma Durga Prasad Department of Computing and Software Engineering, Arba Minch University, Arba Minch, Ethiopia 29 8 3011 3025 13 07 2026

This paper aims to study soft rings using the concept of soft binary operations as a quadruple (ℜ, *, △, P) involving of a non-empty set R and soft binary operations (*, P) and (△, P) satisfying all the ring axioms in softness settings. We study soft rings, along with related concepts like soft subrings and soft ideals. Their properties and relationships between soft rings and classical rings are examined, and elucidated by examples. Furthermore, soft Boolean rings and prime soft ideals are defined and associated theorems are proved.

 Soft sets Soft rings θ-unit element θ-idempotent element θ-nilpotency index Soft ideals access open retracted no