JCGP-Injective Rings With Some Types of Rings


  • Abdullah M. Abdul-Jabbar Department of Mathematics, College of Science, Salahaddin University, Kirkuk Main Street, Erbil, Kurdistan Region, Iraq. Author




JCP-injective rings, JCGP-injective rings, GP-injective rings, Regular rings


The concept of right P-injective rings, which was first introduced by Ming in 1974. As a generalization of right P-injective rings, the notion of right JCP-injective rings, which was first introduced by Junchao in 2009. Now, in the present paper we introduce the notion of right JCGP-injective rings, which is stronger than right GP-injective rings due to Ming in 1985. Some properties, characterizations and main results for right JCGPinjective rings will be finding.


Burton D. M., "A first course in rings and ideals", Addison Wesley Publishing Company, (1970).

Gooderl K. R., "von Neumann regular rings", Pitman (London), (1979).

Huh C., Kim H. K. and Lee Y., "P. P. rings and generalized P. P. rings", J. Pure Appl. Algebra, 167; 3752, (2002). DOI: https://doi.org/10.1016/S0022-4049(01)00149-9

Junchao W., "JCP-injective rings, International Electronic Journal of Algebra", Vol. 6; 1-22, (2009).

Kim N. K., Nam S. B. and Kim J. Y., "On simple GP-injective modules", Comm. Algebra, 23(14); 54375444, (1995). DOI: https://doi.org/10.1080/00927879508825543

Kim N. K., Nam S. B. and Kim J. Y., "On simple singular GP-injective modules", Comm. In Algebra, 27(5); 2087-2096, (1999). DOI: https://doi.org/10.1080/00927879908826551

Lam T.Y., "A first course in non commutative rings", Graduate Texts in Mathematics 131(2 ed), New York, Springer Verlag; pp. xx+385, (2001). DOI: https://doi.org/10.1007/978-1-4419-8616-0

McCoy N. H., "Generalized regular rings", Bull. Amer. Math. Soc. 45; 175-178, (1939). DOI: https://doi.org/10.1090/S0002-9904-1939-06933-4

Ming R.Y.C., "On von Neumann regular rings", Proc. Edinburgh Math. Soc. 19; 89- 91, (1974). DOI: https://doi.org/10.1017/S0013091500015418

Ming R.Y.C., "On regular rings and Artinian rings II", Riv. Math. Univ. Parma., 4(11); 101-109, (1985).

Ming R.Y.C., "On semi-prime and radical rings", Riv. Math. Univ. Parma, 4(12); 167-175, (1986).

Nicholson W. K. and Watters J. F., "Rings with projective socle", Proc. Amer. Math. Soc., 102; 443450, (1988). DOI: https://doi.org/10.1090/S0002-9939-1988-0928957-5

Nicholson W. K. and Yousif M. F., "Weakly continuous and C2-rings", Comm. Algebra, 29(6); 24292466, (2001). DOI: https://doi.org/10.1081/AGB-100002399

Satyanarayana B. H., "On modules with finite Goldie dimension", J. Ramanujan Math. Soc., 5; 61-75, (1990).

Tuganbaev A. A., "Semi regular, weakly regular and π-regular rings", Journal of Mathematical Sciences, 109(3), (2002). DOI: https://doi.org/10.1007/978-94-015-9878-1_4

von Neumann J., "On regular rings", Proc. Nat. Sci. U. S. A. 22; 707-713, (1939). DOI: https://doi.org/10.1073/pnas.22.12.707



How to Cite

JCGP-Injective Rings With Some Types of Rings. (2014). Journal of Zankoy Sulaimani - Part A, 17(1), 17-26. https://doi.org/10.17656/jzs.10357