Ideal Dasar Prima Dalam Aljabar Atas Suatu Ring Komutatif
DOI:
https://doi.org/10.14421/fourier.2018.72.79-86Keywords:
basic ideal, free ideal, non-free algebra, prime basic idealAbstract
Definisi ideal dasar dan ideal bebas dalam aljabar bebas atas ring komutatif dengan elemen satuan adalah ekuivalen. Namun, ideal dasar dalam suatu aljabar tak bebas belum tentu merupakan ideal bebas, sementara ideal bebas pasti ideal dasar. Artikel ini membahas beberapa sifat ideal dasar prima dalam aljabar tak bebas atas ring komutatif dengan elemen satuan.
[The definitions of basic ideal and free ideal in free algebras over a unital commutative ring are equivalen. However, a basic ideal in the non-free algebra is not neceearily a free ideal, while any free ideal is definitely a basic ideal. This paper will discuss some properties of prime basic ideal in non-free algebras over a unital commutative ring.]
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References
[1] K. Wardati, I.E. Wijayanti, S. Wahyuni, 2012, Ideal Mendasar dalam Aljabar Lintasan Leavitt, Prosiding pada Konferensi Nasional Matematika XVI, Jurusam Matematika Universitas Padjadjaran, Bandung, Indonesia, 75-84.
[2] K. Wardati, I.E. Wijayanti, S. Wahyuni, 2014, On Primeness of Path Algebras over a Unital Commutative Ring, JP. Journal of Algebra, Number Theory and Applications, 34(2), 121-138
[3] K. Wardati, I.E. Wijayanti, S. Wahyuni, 2015, On Free Ideals In Free Algebras Over A Commutative Ring, J. Indones. Math. Soc, 21 (1)}, 59-69.
[4] M. Tomforde, 2011, Leavitt Path Algebras with Coefficient in a Commutative Ring, J. Pure. Appl. Algebra, 215, 471-484.
[5] P. A. Grillet, 2007, Abstract Algebra, Graduated Texts in Mathematics, Spinger-Verlag, New York.
[6] R. Wisbauer, 1991, Foundations of Module and Ring Theory, A Handbook for Study and Research, University of Dusseldorf, Gordon and Breach Publisher.
[7] T.Y. Lam, 1991, A First Course in Noncommutative Rings, Springer-Verlag, New York.
[8] W.A. Adkins, S.S. Weintraub, 1999, Algebra an Approach Via Module Theory}, Springer-Verlag NewYork, 1999.
[2] K. Wardati, I.E. Wijayanti, S. Wahyuni, 2014, On Primeness of Path Algebras over a Unital Commutative Ring, JP. Journal of Algebra, Number Theory and Applications, 34(2), 121-138
[3] K. Wardati, I.E. Wijayanti, S. Wahyuni, 2015, On Free Ideals In Free Algebras Over A Commutative Ring, J. Indones. Math. Soc, 21 (1)}, 59-69.
[4] M. Tomforde, 2011, Leavitt Path Algebras with Coefficient in a Commutative Ring, J. Pure. Appl. Algebra, 215, 471-484.
[5] P. A. Grillet, 2007, Abstract Algebra, Graduated Texts in Mathematics, Spinger-Verlag, New York.
[6] R. Wisbauer, 1991, Foundations of Module and Ring Theory, A Handbook for Study and Research, University of Dusseldorf, Gordon and Breach Publisher.
[7] T.Y. Lam, 1991, A First Course in Noncommutative Rings, Springer-Verlag, New York.
[8] W.A. Adkins, S.S. Weintraub, 1999, Algebra an Approach Via Module Theory}, Springer-Verlag NewYork, 1999.
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Published
2018-10-31
How to Cite
Wardati, K. (2018). Ideal Dasar Prima Dalam Aljabar Atas Suatu Ring Komutatif. Jurnal Fourier, 7(2), 79–86. https://doi.org/10.14421/fourier.2018.72.79-86
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