International Journal of Statistics and Applied Mathematics
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International Journal of Statistics and Applied Mathematics

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: 14 | Downloads: 5

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How to cite this article:
Ashok Kumar Pandey. Purity relative to a cyclic module. International Journal of Statistics and Applied Mathematics. 2020; 5(3): 55-58.
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