Abstract
In this paper, we introduce the notions of left (right) Boolean rings and nearrings. We give examples to show that left (right) Boolean rings are not commutative in general. We obtain interrelations among these algebraic structures and get conditions under which the structures are commutative. Finally, we study the concept of derivations on left (right) Boolean rings and nearrings and obtain commutativity results
Highlights
A nearring (N, +, ·) is an algebraic system with binary operations addition and mutiplication satisfying the axioms of a ring, except commutativity of addition and one of the distributive laws
A natural example of right nearring is the set of all mappings from a group (G, +) to itself under addition and composition of mappings
A Boolean ring R is a ring for which x2 = x for all x ∈ R
Summary
A nearring (N, +, ·) is an algebraic system with binary operations addition and mutiplication satisfying the axioms of a ring, except commutativity of addition and one of the distributive laws. A natural example of right nearring is the set of all mappings from a group (G, +) to itself under addition and composition of mappings. In this sequel, N denotes a right nearring. Reddy [27] studied recent developments in Boolean nearrings. Kuncham and Kedukodi [5] studied graph theoretic aspects of nearrings. Kuncham and Bhavanari [12,13] studied equiprime, 3-prime and c-prime fuzzy ideals of nearrings.
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