(n , t)-Presented Modules and (n, t)-Coherent Rings

Dor Celestine Kewir; Francis Fai Mbuntum

doi:https://doi.org/10.14445/22315373/IJMTT-V17P502

International Journal of Mathematics Trends and Technology

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Volume 17 | Number 1 | Year 2015 | Article Id. IJMTT-V17P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V17P502

(n , t)-Presented Modules and (n, t)-Coherent Rings

Dor Celestine Kewir, Francis Fai Mbuntum

Abstract

Coherent rings were first introduced by Chase as a generalization of right Noetherian rings. His characterization has led to several generalizations of this concept. n-coherent rings have been studied by many authors like Glaz S. (1989), Costa (1994), Chen and Ding (1996),Weimin Xue (1999), Dexu Zhou (2004), Zhanmin Zhu(2011) . Some authors have also studied the notion of coherence with respect to a particular torsion theory. Wurfel (1973) characterizes rings which are coherent relative to a faithful hereditary torsion theory and M. F. Jones (1982) extended Wurfel's result to a setting of an arbitrary hereditary torsion theory and used her result to generalize Chase's theorem to the same setting. We introduce the notions of (n, t)-presented modules and (n, t)-coherent rings. Proposition 1.1 of Zhanmin Zhu (2011) and some results obtained by Chen and Ding (1996), are generalized to the setting of an hereditary torsion theory.

Keywords

(n,t)-Presented Modules, (n,t)-flat Modules, (n,t)-FP-Injective Modules, (n,t)-Coherent Rings, (n,t)-FP-Injective Dimensions of Modules

References

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Citation :

Dor Celestine Kewir, Francis Fai Mbuntum, "(n , t)-Presented Modules and (n, t)-Coherent Rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 17, no. 1, pp. 9-15, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V17P502