Tensor product of R-Algebra and R-Homomorphism with M-Injective modules

Dr. Sumit Kumar Dekate

doi:https://doi.org/10.14445/22315373/IJMTT-V19P521

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 19 | Number 3 | Year 2015 | Article Id. IJMTT-V19P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V19P521

Tensor product of R-Algebra and R-Homomorphism with M-Injective modules

Dr. Sumit Kumar Dekate

Citation :

Dr. Sumit Kumar Dekate, "Tensor product of R-Algebra and R-Homomorphism with M-Injective modules," International Journal of Mathematics Trends and Technology (IJMTT), vol. 19, no. 3, pp. 169-172, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V19P521

Abstract

1. If E1 be any M-injective submodule of M, then ØM is isomorphism iff ØE1 is isomorphism, 2. If M is a left R-module then Ø TrM N is isomorphism iff ØM is isomorphism 3. If N and M are two finitely generated module over an artinian ring R and U be any submodule of M such that each simple submodule of U is M-injective then ØM is isomorphism iff ØU is isomorphism

Keywords

M-injective module, Injective modules, Artinian ring, Tensor product, Finitely generated module.

References

[1] F. W. Anderson and K. R. Fuller, Rings and Catagories of modules , New York Springer – Verlag Inc. 1973.
[2] LOUIS HALLE ROWEN, Ring theory.
[3] T. Y. LAM, A first course in noncommutative rings Springer-Verlag.
[4] ANDOR KERTE’SZ, Lectures on artinian ring, Akademiai Kiado, Budapest 1987.