Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

△-CLOSURES OF IDEALS WITH RESPECT TO MODULES

  • Ansari-Toroghy, H. (Department of Mathematics, Faculty of Science, Guilan University) ;
  • Dorostkar, F. (Department of Mathematics, Faculty of Science, Guilan University)
  • Received : 2007.10.23
  • Accepted : 2008.01.23
  • Published : 2008.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

Let M be an arbitrary module over a commutative Noetherian ring R and let ${\triangle}$ be a multiplicatively closed set of non-zero ideals of R. In this paper, we will introduce the dual notion of ${\triangle}$-closure and ${\triangle}$-dependence of an ideal with respect to M and obtain some related results.

Keywords

References

  1. H. Ansari-Toroghy and R.Y. Sharp, Asymptotic behaviour of ideals relative to injective modules over commutative Noetherian rings, Proc. Edinburgh Math. Soc. (2) 34 (1991), 155-160. https://doi.org/10.1017/S0013091500005071
  2. H. Ansari-Toroghy and R.Y. Sharp, Integral closure of ideals relative to injective modules over commutative Noetherian rings, Quart. J. Math. Oxford, (2) 42 (1991), 393-402. https://doi.org/10.1093/qmath/42.1.393
  3. L. Melkersson, P. Schenzel, Asymptotic attached prime ideals related to injective modules, Comm. Algebra (2) 20 (1992), 583-590. https://doi.org/10.1080/00927879208824358
  4. R. Naghipour and M. Sedghi, ${\Delta}-Reductions$ and ${\Delta}-closures$ of ideals with respect to an Artinian module, Communications in Algebra, 34 (2006), 763-777. https://doi.org/10.1080/00927870500388075
  5. L.J. Ratliff, Jr., ${\Delta}-closures$ of ideals and rings, Trans. Amer. Math. Soc., 313 (1989), 221-247.
  6. L.J. Ratliff, Jr. and D. E. Rush, ${\Delta}-Reductions$ of modules, Communications in Algebra, (8) 21 (1993), 2667-2685. https://doi.org/10.1080/00927879308824699
  7. D. Rees and R.Y. Sharp, On a theorem of B. Teissier on multiplicities of ideals in local rings, J. London Math. Soc. (2)18 (1978), 449-463. https://doi.org/10.1112/jlms/s2-18.3.449