Differential projective modules over differential rings, II

Abstract

Differential modules over a commutative differential ring R which are finitely generated projective as ring modules, with differential homomorphisms, form an additive category, so their isomorphism classes form a monoid. We study the quotient monoid by the submonoid of isomorphism classes of free modules with component wise derivation. This quotient monoid has the reduced K₀ of R (ignoring the derivation) as an image and contains the reduced K₀ of the constants of R as its subgroup of units. This monoid provides a description of the isomorphism classes of differential projective R modules up to an equivalence.

Keywords:

• Differential ring
• projective module

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13N15
• Secondary: 12H05; 13C10