$ {n} $-coherent rings in terms of complexes

$ {n} $-coherent rings in terms of complexes

The aim of this paper is to investigate n-coherent rings using complexes. To this end, the concepts of n-injective complexes and $ {n} $-flat complexes are introduced and studied.

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  • [1] D. Bennis, n-X -coherent rings, Int. Electron. J. Algebra. 7 (2010) 128-139.
  • [2] N. Bourbaki, Alg` ebre Commutative, Chapitre 1-2, Masson, Paris, 1961.
  • [3] S. U. Chase, Direct products of modules, Trans. Amer. Math. Soc. 97 (1960) 457-473.
  • [4] T. J. Cheatham, D. R. Stone, Flat and projective character modules, Proc. Amer. Math. Soc. 81 (1981) 175-177.
  • [5] J. L. Chen and N. Q. Ding, On $ {n} $-coherent rings, Comm. Algebra. 24(10) (1996) 3211-3216.
  • [6] L. W. Christensen, H. B. Foxby and H. Holm, Derived Category Methods in Commutative Algebra, 2011.
  • [7] D. L. Costa, Parameterizing families of non-noetherian rings, Comm. Algebra 22 (1994) 3997-4011.
  • [8] N. Q. Ding and L. X. Mao, On a new characterization of coherent rings, Publ. Math. (Debreen), 71 (2007) 67-82
  • [9] E. E. Enochs, J. R. Garc ́ ßa Rozas, Tensor products of complexes, Math. J. Okayama Univ. 39 (1997) 17-39.
  • [10] E. E. Enochs, J. R. Garc ́ ßa Rozas, Flat covers of complexes, J. Algebra 210 (1998) 86-102.
  • [11] E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, (Walter de Gruyter, 2000).
  • [12] J. R. Garc ́ ßa Rozas, Covers and envelopes in the category of complexes of modules, Boca Raton London New York Washington, D.C. (1999).
  • [13] S. Glaz, Commutative Coherent Rings, Lect. Notes Math. 1371, Springer-Verlag, Berlin, 1989. Publishing. (1993) 172-181.
  • [14] B. Stenstr ̈ om, Coherent rings and F P -injective modules, J. London Math. Soc. 2 (1970) 323-329.
  • [15] S. Stenstr ̈ om, Rings of Quotients, New York: Springer-Verlag, 1975.
  • [16] W. V. Vasconcelos, The Rings of Dimension Two, Marcel Dekker, New York, 1976.
  • [17] Z. P. Wang and Z. K. Liu, F P -injective complexes and F P -injective dimension of complexes, J. Aust. Math. Soc. (2011) 1-25.