PERLUASAN SIFAT RANK MATRIKS BUJURSANGKAR ATAS RING KOMUTATIF DITINJAU DARI DETERMINANNYA

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Authors

  • Ismanto Ismanto Universitas Nahdlatul Ulama Sunan Giri

DOI:

https://doi.org/10.32665/james.v1iApril.13

Keywords:

Ideal, Annihilator, Rank of Matrices Over Commutative Ring, Rank Matriks Atas Ring Komutatif

Abstract

This paper is described the properties rank of square matrices over commutative ring if connected with it’s determinant. Rank of n x n matrix over commutative ring is less than n, if  it’s determinant is an element of zero divisor in R. Rank of n x n matrix over commutative ring is n, if it’s determinant is not element of zero divisor in R.

 

Makalah ini membahas sifat-sifat rank matriks bujursangkar atas ring komutatif jika dihubungkan dengan determinannya. Rank matriks atas ring komutatif ukuran n x nlebih kecil dari n, jika determinannya merupakan anggota pembagi nol di R.Rank matriks atas ring komutatif ukuran n x nsama dengan n, jika determinannya bukan anggota pembagi nol di R.

References

[1] Bhattacharya, P.B., Jain, S.K., &Nagpaul, S.R., Basic Abstract Algebra, Press Sydicate, Australia (1990).
[2] Brown, W.C., Matrices over Commutative Rings, Marcel Dekker Inc, New York (1993).
[3] Durbin, J.R., Modern Algebra An Introduction, John Willey and Sons Inc. New York (1992).
[4] Leon, S.J., Aljabar Linier dan Aplikasinya, Erlangga, Jakarta (2001).
Mathematics Journal

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Published

2018-04-15

How to Cite

[1]
I. Ismanto, “PERLUASAN SIFAT RANK MATRIKS BUJURSANGKAR ATAS RING KOMUTATIF DITINJAU DARI DETERMINANNYA”, JaMES, vol. 1, no. 1, pp. 21–28, Apr. 2018.

Issue

Vol. 1 No. 1 (2018): Journal of Mathematics Education and Science

Section

Articles

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Abstract View: 345, PDF Download: 367