Schanuel's Lemma in P-Poor Modules
AbstractModules 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.
Copyright (c) 2019 Iqbal Maulana
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work