Google scholar arxiv informatics ads IJAIS publications are indexed with Google Scholar, NASA ADS, Informatics et. al.

Call for Paper

-

November Edition 2021

International Journal of Applied Information Systems solicits high quality original research papers for the November 2021 Edition of the journal. The last date of research paper submission is October 15, 2021.

Empirical Study of Cocyclic Copurity and the Dualization of Cyclic Purity

Md. Arshaduzzaman, Yusuf Perwej, Ashwani Kumar Sinha. Published in Information Sciences

International Journal of Applied Information Systems
Year of Publication: 2016
Publisher: Foundation of Computer Science (FCS), NY, USA
Authors: Md. Arshaduzzaman, Yusuf Perwej, Ashwani Kumar Sinha
10.5120/ijais2016451547
Download full text
  1. Md. Arshaduzzaman, Yusuf Perwej and Ashwani Kumar Sinha. Empirical Study of Cocyclic Copurity and the Dualization of Cyclic Purity. International Journal of Applied Information Systems 10(9):15-18, May 2016. URL, DOI BibTeX

    @article{10.5120/ijais2016451547,
    	author = "Md. Arshaduzzaman and Yusuf Perwej and Ashwani Kumar Sinha",
    	title = "Empirical Study of Cocyclic Copurity and the Dualization of Cyclic Purity",
    	journal = "International Journal of Applied Information Systems",
    	issue_date = "May 2016",
    	volume = 10,
    	number = 9,
    	month = "May",
    	year = 2016,
    	issn = "2249-0868",
    	pages = "15-18",
    	numpages = 4,
    	url = "http://www.ijais.org/archives/volume10/number9/890-2016451547",
    	doi = "10.5120/ijais2016451547",
    	publisher = "Foundation of Computer Science (FCS), NY, USA",
    	address = "New York, USA"
    }
    

Abstract

In this paper, we discussed about the Co-cylic co-purity of the dualization of cyclic purity i. e., the Co-purity versus Cohn’s purity and the C-purity versus CP and the Co-cyclic co-purity versus purity and Co-cyclic co-purity versus C-purity. Many examples are given to show that the concepts of Co-cyclic Co-purity and Cyclic purity are independent.

Reference

  1. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag New York. Heidelberg. Berlin,(1991).
  2. D. P. Choudhary and K. Tewari, Tensor purities, cyclic quasiprojective and Co-cyclic copurity, Gomm. in Alg.,7(1979), 1559-1572.
  3. P. M. Conn, On the free product of associative rings-I.Math.Z.,71(1959),380-398.
  4. K. Divani-Aazar, M. A. Esmkhani and M.Tousi, Some criteria of cyclically pure injective modules, Journal of Algebra., 304(2006), 367-381.
  5. L. Fuchs, Infinite Abelian Groups, Academic Press New York & London.(1970)
  6. V. A. Hiremath, Cofinitcly generated and cofinitely related modules, Acta.Math. Acad.Sci.Hungar.,39(1982),1-9. Study of Cocyclic Copurity and the Dualization of Cyclic Purity : Ashwani Kumar Sinha
  7. V. A. Hiremath, Hopure submodules, Acta.Math.Hungar.,44(1984), 3-12.
  8. J. P. Jans.On co-Noetherian rings. J.London Math. Soc.(2)l (1969) ,588-590.
  9. T. Y. Lam, A First Course in Noncommutative Rings, Springer publications (1990).
  10. S. S. Mat-Lane, Ilomology, Springer(1967).
  11. N. H. McCoy, The Theory of Rings.The Macmillan company., New York,(1967).
  12. M. S. Osborne, Basic Homological Algebra., Springer-Verlag New York, Inc (2000).
  13. K L. Osofisky. A Generalization of a Quasi- Frohenius rings, Journal of Algebras, 4 (1966), 373-387.
  14. B. L. Osofsky, Cyclic injective modules of full linear rings, Proc.Amer..Math.Soc. 17(1966), 247-253.
  15. J. Simmons,Cyclic purity, a generalization of purity for modules. Houston J.Math. 13, No.l (1987), 135-150.
  16. B. Stenstrom, Pure Submodules, Arkiv for Mat. 7(1967), 159-171.
  17. B. Stenstrom,Rings of Quotients, Springer- Verlag , New York, Heidelberg, Berlin (1975).
  18. P. Vamos,On the dual of the notion of finitely generated, J.London Math.Soc., 43 (1968), 643-646.
  19. R. B. Warfield Jr., Purity and algebraic compactness for modules, Pacific J.Math. 28(3) (1969), 699-719.
  20. R. Wisbauer, Foundations of Modules and Ring Theory, Gordon and Breach Science Publishers (2007).

Keywords

Cyclic Purity, Co-Cyclic Copurity, Cohn's Purity, Projective, Co-Finitly, Polynomial, Ring, R-Module.