Gardner Problem Revisited: Further Properties of Indah Radical

Radical theory arises naturally from the study of non-commutative rings and plays a central role in the structural analysis of ring classes. Among the radical classes that have received considerable attention are the prime radical β and the IndaH radical , whose relationship is closely related to the Gardner conjecture. While several structural properties of β are well established, the corresponding properties of have remained less clear. In this paper, we investigate the IndaH radical using deductive arguments and structural analysis within the framework of radical theory. In particular, we examine whether satisfies corner-hereditariness, corner-strictness, very corner-hereditariness, and the hereditary phantom corner (HPC) property. We show that possesses all four properties, thereby placing it in closer structural alignment with the prime radical β. The results are obtained under standard assumptions on associative rings and radical classes.