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Abstract
Let A be a free R-algebra where R is a unital commutative ring. An ideal I in A is called a free ideal if it is a free R-submodule with the basis contained in the basis of A. The denition of free ideal and basic ideal in the free R-algebra are equivalent. The free ideal notion plays an important role in the proof of some special properties of a basic ideal that can characterize the free R-algebra. For example, a free R-algebra A is basically semisimple if and only if it is a direct sum of minimal basic ideals in A: In this work, we study the properties of basically semisimple free R-algebras.
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References
- Abrams,G, Aranda Pino,G., Perera,F., Molina,S. M., Chain conditions for Leavitt path algebras, Forum Math. (To appear.)
- Grillet, P. A., Abstract Algebra, Graduated Texts in Mathematics, Spinger-Verlag, New
- York, (2007).
- Lam, T.Y., A First Course in Noncommutative Rings, Springer-Verlag, New York, (1991).
- Tomforde, M., Leavitt Path Algebras with Coecient In A Commutative Ring, J. Pure Appl. Algebra 215 (2011), 471-484.
- Wardati, K., Wijayanti, I.E., Wahyuni, S., On Basic Ideal in Leavitt Path Algebra (In Indonesia), Proceedings of Mathematical National Conference XVI, Mathematics Departement, Padjadjaran University, Bandung, Indonesia, ISBN 978-602-19590-2-2, (2012), 75-84.
- Wardati, K., Wijayanti, I.E., Wahyuni, S., Basically Semisimple of Leavitt Path Algebra on Acyclic Finite Graph (In Indonesia), Presented in "Seminar Nasional dan Workshop Aljabar dan Pembelajarannya", Mathematics Departement, Universitas Negeri Malang, Indonesia, 2013.
- Wisbauer, R., Foundations of Module and Ring Theory, Gordon and Breach Publishers, 1991.
References
Abrams,G, Aranda Pino,G., Perera,F., Molina,S. M., Chain conditions for Leavitt path algebras, Forum Math. (To appear.)
Grillet, P. A., Abstract Algebra, Graduated Texts in Mathematics, Spinger-Verlag, New
York, (2007).
Lam, T.Y., A First Course in Noncommutative Rings, Springer-Verlag, New York, (1991).
Tomforde, M., Leavitt Path Algebras with Coecient In A Commutative Ring, J. Pure Appl. Algebra 215 (2011), 471-484.
Wardati, K., Wijayanti, I.E., Wahyuni, S., On Basic Ideal in Leavitt Path Algebra (In Indonesia), Proceedings of Mathematical National Conference XVI, Mathematics Departement, Padjadjaran University, Bandung, Indonesia, ISBN 978-602-19590-2-2, (2012), 75-84.
Wardati, K., Wijayanti, I.E., Wahyuni, S., Basically Semisimple of Leavitt Path Algebra on Acyclic Finite Graph (In Indonesia), Presented in "Seminar Nasional dan Workshop Aljabar dan Pembelajarannya", Mathematics Departement, Universitas Negeri Malang, Indonesia, 2013.
Wisbauer, R., Foundations of Module and Ring Theory, Gordon and Breach Publishers, 1991.