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<p>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.</p>

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Differential Modules Toward Derived Functors

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Li Qiao,
  • Jun Pei

摘要

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.