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 


Abstract

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.


Key Words : JCP-injective rings, JCGP-injective rings, GP-injective rings, regular rings

References:

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

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

[3]    Huh C., Kim H. K. and Lee Y., "P. P. rings and generalized P. P. rings", J. Pure Appl. Algebra, 167; 3752, (2002).

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

[5]    Kim N. K., Nam S. B. and Kim J. Y., "On simple GP-injective modules", Comm. Algebra, 23(14); 54375444, (1995).

[6]    Kim N. K., Nam S. B. and Kim J. Y., "On simple singular GP-injective modules", Comm. In Algebra, 27(5); 2087-2096, (1999). 

[7]    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).

[8]    McCoy N. H., "Generalized regular rings", Bull. Amer. Math. Soc. 45; 175-178, (1939).

[9]    Ming R.Y.C., "On von Neumann regular rings", Proc. Edinburgh Math. Soc. 19; 89- 91, (1974). 

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

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

[12]  Nicholson W. K. and Watters J. F., "Rings with projective socle", Proc. Amer. Math. Soc., 102; 443450, (1988). 

[13]  Nicholson W. K. and Yousif M. F., "Weakly continuous and C2-rings", Comm. Algebra, 29(6); 24292466, (2001). 

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

[15]  Tuganbaev A. A., "Semi regular, weakly regular and π-regular rings", Journal of Mathematical Sciences, 109(3), (2002). 

[16]  von Neumann  J., "On regular rings", Proc. Nat. Sci. U. S. A. 22; 707-713, (1939).