Existence of unimodular elements and cancellation of projective modules over Rees-like algebras and its various extensions

Key Points

• This research aims to investigate unimodular elements and their role in the cancellation of projective modules in Rees-like algebras.
• Analysis of unimodular elements in the context of Rees-like algebras.
• Study of cancellation properties of projective modules under various algebraic extensions.
• Identified conditions under which unimodular elements exist in Rees-like algebras.
• Demonstrated significant cancellation properties for specific projective modules over these algebras.