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- W2515569713 abstract "Throughout this paper, R is a commutative Notherian ring with non-zero identity and M is a finitely generated R-module. This paper is concerned with a certain complex C(U(x),M) of R-modules and R-homomorphism which involves modules of generalized fractions derived from M and the sequence x1, x2, . . . , xn. The complex is described as follows: for each i ∈ N (throughout we use N to denote the set of positive integers). Set U(x)i = {(x1 1 , x2 2 , . . . , xi i ) | ∃j, 0 ≤ j ≤ i s.t. α1, . . . , αj ∈ N, and αj+1 = · · · = αi = 0}, where xr is interpreted as xn whenever r > n. Then, for each i ∈ N, U(x)i is a triangular subset [4,2.1] of R. We can [2, page 420] from the complex 0 → M e0 −→ U(x)−1 1 M e 1 −→ · · · ei −→ U(x)−i−1 i+1 M e i+1 −→ · · · of R-modouls and R-homomorphisms, which we denote by C(U(x),M). Here U(x)−i i M is modoule of generalized fractions of M with respect to the triangular subset U(x)i of R , and the homomorphisms e (i ≥ 0) are given by the following formulas. e(b) = b (1) for all b ∈ M and, for each i ∈ N," @default.
- W2515569713 created "2016-09-16" @default.
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- W2515569713 date "2007-01-01" @default.
- W2515569713 modified "2023-09-25" @default.
- W2515569713 title "Tot(M) and modules of generalized fractions" @default.
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- W2515569713 doi "https://doi.org/10.12988/ija.2007.07056" @default.
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