Abstract
Rings and fields are significant algebraic structures in algebra and both of them are based on the group structure. In this paper, we attempt to extend the notion of a neutrosophic triplet group to a neutrosophic triplet ring and a neutrosophic triplet field. We introduce a neutrosophic triplet ring and study some of its basic properties. Further, we define the zero divisor, neutrosophic triplet subring, neutrosophic triplet ideal, nilpotent integral neutrosophic triplet domain, and neutrosophic triplet ring homomorphism. Finally, we introduce a neutrosophic triplet field.
Highlights
The concept of a ring first arose from attempts to prove Fermat’s last theorem [1], starting withRichard Dedekind in the 1880s
Mathematicians have devised various notions to break rings into smaller, more understandable pieces, such as ideals, quotient rings, and simple rings. In addition to these abstract properties, ring theorists make various distinctions between the theories of commutative rings and noncommutative rings, the former belonging to algebraic number theory and algebraic geometry
A rich theory has been developed for a certain special class of commutative rings, known as fields, which lies within the realm of field theory
Summary
The concept of a ring first arose from attempts to prove Fermat’s last theorem [1], starting with. A very active mathematical discipline, studies rings in their own right. Mathematicians have devised various notions to break rings into smaller, more understandable pieces, such as ideals, quotient rings, and simple rings In addition to these abstract properties, ring theorists make various distinctions between the theories of commutative rings and noncommutative rings, the former belonging to algebraic number theory and algebraic geometry. The generalization of classical sets [9], fuzzy sets [11], and intuitionistic fuzzy sets [10], etc., is the neutrosophic set This mathematical tool is used to handle problems consisting of uncertainty, imprecision, indeterminacy, inconsistency, incompleteness, and falsity.
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