International Journal of Statistics and Applied Mathematics
  • Printed Journal
  • Indexed Journal
  • Refereed Journal
  • Peer Reviewed Journal

2020, Vol. 5, Issue 3, Part A

Purity relative to a cyclic module

Author(s): Ashok Kumar Pandey

Abstract: We study relative projectivity and injectivity classes of exact sequences with respect to the classes of cyclic modules. A characterization of cyclic pure exact sequences has given in terms of exactness of a certain sequence of submodules of the modules appearing in the given sequence. We also study the concept of relative divisibility of elements in submodules (known as - purity). We give the generalization of the proposition of Stenstrom. We characterize the preservation of exactness by cyclic modules where be a left ideal of the ring . We also relate the purity in Quasi- projective module [9]. We also try to define Copure for a class of modules and co-relate Copure injective or Copure projective with it. We derive some results dualize certain results of R.B. Warfield.

Pages: 55-58 | Views: 571 | Downloads: 12

Download Full Article: Click Here
How to cite this article:
Ashok Kumar Pandey. Purity relative to a cyclic module. Int J Stat Appl Math 2020;5(3):55-58.

Call for book chapter
International Journal of Statistics and Applied Mathematics