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A study on semigroups in which the radical of every n-interior ideal is a subsemigroup

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This paper characterizes when the radical of every interior ideal forms a subsemigroup, indicating profound connections among semigroup theory.

The study identifies conditions for the radical of every interior ideal to be a subsemigroup, enhancing understanding of semigroup structures.
Radicals of various types of ideals—like right, left, and two-sided ideals—are characterized within semigroups, impacting their structural analysis.
Connections between ideals and radicals are explored, revealing how they contribute to the algebraic framework of semigroups.
Understanding the radical of the interior ideals furthers our grasp of their role in the overarching theory of semigroups.

Tiprachot et al. (2025) studied this question.

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This paper characterizes when the radical of every interior ideal forms a subsemigroup, indicating profound connections among semigroup theory.