November 30, 2025Open Access

Splitting criteria for projective modules over polynomial algebras

Key Points

Proving the monic inversion principle addresses an open question in algebraic theory, leading to advancements in module theory.
The exploration focuses on finitely generated projective modules over polynomial algebras and their applications in affine algebras.
Analysis reveals connections between projective modules and ideals in the setting of finitely generated rings over algebraically closed fields.
The findings may enable further exploration of algebraic structures and their properties in mathematical research.

Abstract

Abstract This article investigates the splitting problem for finitely generated projective modules over affine algebras over algebraically closed fields and their polynomial extensions. We then address an open question due to M. Roitman on monic inversion principle for projective modules and prove it in the affirmative for finitely generated rings. For affine algebras over , we prove a monic inversion principle for ideals. We also exhibit some applications.

Splitting criteria for projective modules over polynomial algebras

Key Points

Abstract

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