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

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2015 by IJMTT Journal
Volume-19 Number-3
Year of Publication : 2015
Authors : Dr. Sumit Kumar Dekate
  10.14445/22315373/IJMTT-V19P521

MLA

Dr. Sumit Kumar Dekate"Tensor product of R-Algebra and R-Homomorphism with M-Injective modules", International Journal of Mathematics Trends and Technology (IJMTT). V19(3):169-172 March 2015. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

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

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.

Keywords
M-injective module, injective modules, artinian ring, tensor product, finitely generated module.