Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

DUAL BASS NUMBERS AND CO-COHEN MACAULAY MODULES

  • Li, Lingguang (School of Mathematical Sciences Tongji University)
  • Received : 2017.01.31
  • Accepted : 2017.06.08
  • Published : 2018.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we show that the co-localization of co-Cohen Macaulay modules preserves co-Cohen Macaulayness under a certain condition. In addition, we give a characterization of co-Cohen Macaulay modules by vanishing properties of the dual Bass numbers of modules.

Keywords

References

  1. N. T. Cuong, N. T. Dung, and L. T. Nhan, Top local cohomology and the catenaricity of the unmixed support of a finitely generated module, Comm. Algebra 35 (2007), no. 5, 1691-1701. https://doi.org/10.1080/00927870601169366
  2. N. T. Cuong and L. T. Nhan, On representable linearly compact modules, Proc. Amer. Math. Soc. 130 (2002), 1927-1936. https://doi.org/10.1090/S0002-9939-01-06298-0
  3. N. T. Cuong and L. T. Nhan, On the Noetherian dimension of Artinian modules, Vietnam J. Math. 30 (2002), 121-130.
  4. E. Enochs and J. Z. Xu, On invariants dual to the Bass numbers, Proc. Amer. Math. Soc. 125 (1997), no. 4, 951-960. https://doi.org/10.1090/S0002-9939-97-03662-9
  5. D. Kirby, Dimension and length for Artinian modules, Quart. J. Math. Oxford Ser. (2) 41 (1990), no. 164, 419-429. https://doi.org/10.1093/qmath/41.4.419
  6. L. Li, Vanishing properties of dual Bass numbers, Algebra Colloq. 21 (2014), no. 1, 167-180. https://doi.org/10.1142/S1005386714000133
  7. L. Melkersson and P. Schenzel, The co-localization of an Artinian module, Proc. Edinburgh Math. Soc. (2) 38 (1995), no. 1, 121-131. https://doi.org/10.1017/S0013091500006258
  8. R. N. Roberts, Krull dimension for Artinian modules over quasi local commutative rings, Quart. J. Math. Oxford Ser. (2) 26 (1975), no. 103, 269-273. https://doi.org/10.1093/qmath/26.1.269
  9. R. Y. Sharp, A method for the study of Artinian modules, with an application to asymptotic behaviour, In: Commutative algebra (Berkeley, CA, 1987), 443-465, Math. Sci. Res. Inst. Publ., 15, Springer, New York, 1989.
  10. Z. Tang, Co-Cohen-Macaulay modules and multiplicities for Arinian modules, J. Suzhou Univ. (natural science) 12 (1996), 15-26.
  11. Z. Tang and H. Zakeri, Co-Cohen-Macaulay modules and modules of generalized fractions, Comm. Algebra 22 (1994), no. 6, 2173-2204. https://doi.org/10.1080/00927879408824960