COUSIN COMPLEXES AND GENERALIZED HUGHES COMPLEXES

  • Kim, Dae-Sig (Department of Mathematics, Dongshin University, Naju 520-714) ;
  • Song, Yeong-Moo (Department of Mathematical Education, Sunchon National University, Sunchon 540-742)
  • Published : 1994.07.01

Abstract

In this paper, the ring A will mean a commutative Noetherian ring with non-zero multiplicative identity, it is understood that the ring homomorphisms respect identity elements and M will denote an A-module. Throughout this paper A and B will denote rings, $f : A \to B$ a ring homomorphism. C(A) (resp. C(B)) presents the category of all A-modules (resp. B-modules) and A-homomorphisms (resp. B-homorphisms) between them. The following ideas will be used without further explanation. B can be regarded as an A-module by means of f and $M\otimesB$ can be regarded as a B-module in the natural way. Furthermore the restriction of scalars provides a functor from C(B) to C(A).

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