Schanuel's Lemma in P-Poor Modules
Modules are a generalization of the vector spaces of linear algebra in which the “scalars” are allowed to be from a ring with identity, rather than a field. In module theory there is a concept about projective module, i.e. a module over ring R in which it is projective module relative to all modules over ring R. Next, there is the fact that every module over ring R is projective module relative to all semisimple modules over ring R. If P is a module over ring R which it’s projective relative only to all semisimple modules over ring R, then P is called p-poor module. In the discussion of the projective module, there is a lemma associated with the equivalence of two modules K1 and K2 provided that there are two projective modules P1 and P2 such that is isomorphic to . That lemma is known as Schanuel’s lemma in projective modules. Because the p-poor module is a special case of the projective module, then in this paper will be discussed about Schanuel’s lemma in p-poor modules
A. N. Alahmadi, M. Alkan, and S. R. Lopez-Permouth, “Poor Modules: The Opposite of Injectivity,” Glasgow Mathematical Journal 52A, pp. 7-17, 2010.
C. Holston, S. R. Lopez-Permouth, and N. O. Ertas, “Rings Whose Modules Have Maximal Or Minimal Projectivity Domain,” Journal of Pure and Applied Algebra 216, pp. 673-678, 2012.
F. W. Anderson and K. R. Fuller, Rings and Categories of Modules (Second Edition), New York, 1992.
I. Kaplansky, “Fields and Rings (Second Edition),” Chicago Lectures in Mathematics Series, pp. 165-168, 1972.
F D Lestari et al 2019 J. Phys.: Conf. Ser. 1211 012053
R. Wisbauer, Foundations of Module and Ring Theory, Germany, 1991.
W. A. Adkins and S. H. Weintraub, Algebra An Approach via Module Theory, New York, 1992.
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