Differential Modules Toward Derived Functors

Abstract

The notion of differential algebra of weight λ unifies those of usual differential algebras of zero weight and difference algebras. In this paper, we study modules over differential algebra of weight λ, with emphasis on the role played by the differential operators and the difference between differential modules and modules over an algebra in the usual sense. We introduce the concepts of free, projective, injective and flat differential modules. Furthermore, we present a construction of free differential modules and show that there are enough projective, injective and flat differential modules to provide the corresponding resolutions for derived functors.

Keywords

Differential algebra / differential module / free module / projective module / injective module / flat module / 16W99 / 16S10 / 16T10 / 16T30

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Peking University