Research Article
Empirical Study of Cocyclic Copurity and the Dualization of Cyclic Purity
|
International Journal of Applied Information Systems
Foundation of Computer Science (FCS), NY, USA
|
| Volume 10 - Issue 9 |
| Published: May 2016 |
| Authors: Md. Arshaduzzaman, Yusuf Perwej, Ashwani Kumar Sinha |
10.5120/ijais2016451547
|
Md. Arshaduzzaman, Yusuf Perwej, Ashwani Kumar Sinha . Empirical Study of Cocyclic Copurity and the Dualization of Cyclic Purity. International Journal of Applied Information Systems. 10, 9 (May 2016), 15-18. DOI=10.5120/ijais2016451547
@article{ 10.5120/ijais2016451547,
author = { Md. Arshaduzzaman,Yusuf Perwej,Ashwani Kumar Sinha },
title = { Empirical Study of Cocyclic Copurity and the Dualization of Cyclic Purity },
journal = { International Journal of Applied Information Systems },
year = { 2016 },
volume = { 10 },
number = { 9 },
pages = { 15-18 },
doi = { 10.5120/ijais2016451547 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2016
%A Md. Arshaduzzaman
%A Yusuf Perwej
%A Ashwani Kumar Sinha
%T Empirical Study of Cocyclic Copurity and the Dualization of Cyclic Purity%T
%J International Journal of Applied Information Systems
%V 10
%N 9
%P 15-18
%R 10.5120/ijais2016451547
%I Foundation of Computer Science (FCS), NY, 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.
References
- F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag New York. Heidelberg. Berlin,(1991).
- D. P. Choudhary and K. Tewari, Tensor purities, cyclic quasiprojective and Co-cyclic copurity, Gomm. in Alg.,7(1979), 1559-1572.
- P. M. Conn, On the free product of associative rings-I.Math.Z.,71(1959),380-398.
- K. Divani-Aazar, M. A. Esmkhani and M.Tousi, Some criteria of cyclically pure injective modules, Journal of Algebra., 304(2006), 367-381.
- L. Fuchs, Infinite Abelian Groups, Academic Press New York & London.(1970)
- 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
- V. A. Hiremath, Hopure submodules, Acta.Math.Hungar.,44(1984), 3-12.
- J. P. Jans.On co-Noetherian rings. J.London Math. Soc.(2)l (1969) ,588-590.
- T. Y. Lam, A First Course in Noncommutative Rings, Springer publications (1990).
- S. S. Mat-Lane, Ilomology, Springer(1967).
- N. H. McCoy, The Theory of Rings.The Macmillan company., New York,(1967).
- M. S. Osborne, Basic Homological Algebra., Springer-Verlag New York, Inc (2000).
- K L. Osofisky. A Generalization of a Quasi- Frohenius rings, Journal of Algebras, 4 (1966), 373-387.
- B. L. Osofsky, Cyclic injective modules of full linear rings, Proc.Amer..Math.Soc. 17(1966), 247-253.
- J. Simmons,Cyclic purity, a generalization of purity for modules. Houston J.Math. 13, No.l (1987), 135-150.
- B. Stenstrom, Pure Submodules, Arkiv for Mat. 7(1967), 159-171.
- B. Stenstrom,Rings of Quotients, Springer- Verlag , New York, Heidelberg, Berlin (1975).
- P. Vamos,On the dual of the notion of finitely generated, J.London Math.Soc., 43 (1968), 643-646.
- R. B. Warfield Jr., Purity and algebraic compactness for modules, Pacific J.Math. 28(3) (1969), 699-719.
- R. Wisbauer, Foundations of Modules and Ring Theory, Gordon and Breach Science Publishers (2007).
Index Terms
Keywords