DEKOMPOSISI MODUL AUTOMORFISMA INVARIAN ATAS MODUL KUASI-INJEKTIF DAN MODUL SQUARE-FREE

Authors

  • Inne Syafrian Putri UIN Sunan Gunung Djati Bandung

DOI:

https://doi.org/10.15575/km.v1i2.10215

Keywords:

modul automorfisma invarian, submodul essensial, modul kuasi-injektif, modul square-free

Abstract

Misalkan  adalah modul atas ring . Injektif hull dari , dinotasikan , adalah suatu modul injektif yang memuat  sebagai submodul essensialnya. Jika  invarian dibawah sebarang  automorfisma dari  maka  disebut modul automorfisma invarian. Isomorfisma diantara dua submodul essensial dari modul automorfisma invarian  dapat diperluas menjadi endomorfisma atau automorfisma dari . Komponen langsung dari modul automorfisma invarian juga merupakan modul automorfisma invarian.  Dalam tulisan ini dibuktikan bahwa modul automorfisma invarian dapat didekomposisi atas modul kuasi-injektif dan modul square-free yang saling ortogonal dan relatif injektif.

Author Biography

Inne Syafrian Putri, UIN Sunan Gunung Djati Bandung

Matematika FST UIN SGD Bandung

References

Noyan Er, Surjeet Singh, Ashish K. Srivastava. Rings and modules which are stable under automorphisms of their injective hulls.J. Algebra 379 (2013) 223-229.

T.K. Lee, Y. Zhou. Modules which are invariant under automorphisms of their injective hulls. J. Algebra Appl. 12(2)(2013).

D.S. Passman. 1991. A Course in Ring Theory. AMS. USA.

F.W. Anderson, K.R. Fuller. 1974. Rings and Categories of Modules. Springer-Verlag. New York.

Surjeet Singh, Ashish K. Srivastava. Rings of invariant module type and automorphisminvariant modules.

M. E. Keating. 1998. A firts course in module theory. Imperial College Press. London.

Sri Wahyuni, dkk. 2016. Teori Ring dan Modul. Gadjah Mada University Press. Yogyakarta.

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Published

2020-11-30

Issue

Vol. 1 No. 2 (2020): Khazanah Multidisiplin Vol 1, No 2 November (2020)

Section

Articles

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