What question did this study set out to answer?

The research aims to explore the properties of S-quasi-invertible elements and their relationship with S-nilpotent elements in commutative rings.

July 13, 2026Mathematica SlovacaOpen Access

S -quasi-invertible elements, the S -Jacobson radical, and the S -quasi-inverse graph

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Introduces S-quasi-invertible elements in commutative rings and explores their properties.

The research aims to explore the properties of S-quasi-invertible elements and their relationship with S-nilpotent elements in commutative rings.
Introduced S-quasi-invertible elements in commutative ring R with a multiplicatively closed subset S.
Proved the relationship between elements in Q_S(R) and S-invertible elements.
Established the structure and properties of the S-quasi-inverse graph, including cliques and chromatic number.
Demonstrated that N_S(R) ⊆ J_S(R) ⊆ Q_S(R) holds under suitable assumptions.
Characterized S-nilpotent-clean elements, and found J_S(R) = N_S(R) in suitable rings.
Established basic structural results for the S-quasi-inverse graph, including findings on diameter and completeness.

Abouhalaka et al. (2026) studied this question.

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