Generalizations of N-Injective Modules
Keywords:
P-injective, epp-ring, f-injective, Artinian, Noetherian
Abstract
Any left R-module M is said to be p-injective if for every principal left ideal I of R and any R-homomorphism g : I → M, there exists y ∈ M such that g(b) = by for all b in I. We find that RM is p-injective iff for each r ∈ R, x ∈ M if x / ∈ rM then there exists c ∈ R with cr = 0 and cx 6= 0. A ring R is said to be epp-ring if every projective R-module is p-injective. Any ring R is right epp-ring iff the trace of projective right R-module on itself is p-injective. A left epp-ring which is not right epp-ring has been constructed.
References
F.W.Anderson and K.R.Fuller, Rings and categories of Modules, Springer-Verlag, New York, Heidelberg, (1974).
R.R.Colby, Rings which have flat Injective Modules, J. Algebra, 35(1975), 239-252.
G.O.Michler and O.E.Villamayor, On Rings Whose Simple Modules are Injective, J. Algebra, 25(1973), 185-201.
R.Y.C.Ming, On V-rings and Prime Rings, J. Algebra, 62(1980), 13-20.
B.Zimmermann-Huisgen, Endomorphism Rings of Self Generators, Pacific J. Math., 61(1)(1975), 587-602.
R.R.Colby, Rings which have flat Injective Modules, J. Algebra, 35(1975), 239-252.
G.O.Michler and O.E.Villamayor, On Rings Whose Simple Modules are Injective, J. Algebra, 25(1973), 185-201.
R.Y.C.Ming, On V-rings and Prime Rings, J. Algebra, 62(1980), 13-20.
B.Zimmermann-Huisgen, Endomorphism Rings of Self Generators, Pacific J. Math., 61(1)(1975), 587-602.
How to Cite
D.S.Singh. (2016). Generalizations of N-Injective Modules. International Journal of Current Research in Science and Technology, 2(1), 21-24. Retrieved from https://crst.gfer.org/index.php/crst/article/view/53
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