• σ- PURITY AND σ- REGULAR RINGS AND MODULES

ASHOK KUMAR PANDEY*

Abstract


The aim of this paper is to relativize the concept of  purity and σ - purity defined and studied by Azumaya [6] with respect to an arbitrary hereditary torsion theory given by a left exact torsion radical  and also relates these concepts with the notions of  purity as given by B. B. Bhattacharya and D. P. Choudhury [7]. We also develope the theory of  purity and  purity relative to a torsion theory with radical  where  is a finitely generated or cyclic  module and  is an  matrix determined by a system of linear equations  where  (a left  module) for each  and  are unknowns, which is weaker than the usual purity and given a sufficient condition for these two coincide. In this present paper we relativize the concept of the   pure and  blatness of a module. We also discuss about  regular modules and weakly  regular modules and its inter relationship. We also discuss about finitely generated  blat modules and its condition for  projectivity in Noetherian ring.


Keywords


Left R- modules,M- purity, (M,σ)- purity, σ- pure modules, (μ,σ)- purity, σ- flat modules, σ- regular modules, weakly σ- regular modules, σ- projective modules.

Full Text:

PDF

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
© 2011-2020 Research Journal of Pure Algebra (RJPA)
Copyright Agreement & Authorship Responsibility
HTML Counter
Counter