Generalization of Schur's Lemma in Ring Representations on Modules over a Commutative Ring

Authors

  • Na'imah Hijriati 1. Dept. of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia. 2. Dept. of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lambung Mangkurat, Banjarmasin, Indonesia. https://orcid.org/0000-0002-7622-8816
  • Sri Wahyuni Dept. of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia.
  • Indah Emilia Wijayanti Dept. of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia.

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i3.3285

Keywords:

Representation of ring on module, Generalized Schur's Lemma, Ring homomorphism.

Abstract

Let $ R, S $ be rings with unity, $ M $ a module over $ S $, where $ S $ a commutative ring, and $ f \colon R \rightarrow S $ a ring homomorphism. A ring representation of $ R $ on $ M $ via $ f $ is a ring homomorphism $ \mu \colon R \rightarrow End_S(M) $, where $ End_S(M) $ is a ring of all $ S $-module homomorphisms on $ M $. One of the important properties in representation of rings is the Schur's Lemma.  The main result of this paper is partly the generalization of Schur's Lemma in representations of rings on modules over a commutative ring

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Published

2018-07-31

Issue

Vol. 11 No. 3: (July 2018)

Section

Approximation Theory

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How to Cite

Generalization of Schur’s Lemma in Ring Representations on Modules over a Commutative Ring. (2018). European Journal of Pure and Applied Mathematics, 11(3), 751-761. https://doi.org/10.29020/nybg.ejpam.v11i3.3285