ON FREE IDEALS IN FREE ALGEBRAS OVER A COMMUTATIVE RING
| Main Authors: | Wardati, Khurul; Departement of Mathematics UIN Sunan Kalijaga Yogyakarta, Wijayanti, Indah Emilia; Department of Mathematics, UGM, Yogyakarta, Wahyuni, Sri; Department of Mathematics, UGM, Yogyakarta |
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| Format: | Article application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
IndoMS
, 2015
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| Subjects: | |
| Online Access: |
http://www.jims-a.org/index.php/jimsa/article/view/170 http://www.jims-a.org/index.php/jimsa/article/downloadSuppFile/170/459 |
Daftar Isi:
- 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.DOI : http://dx.doi.org/10.22342/jims.21.1.170.59-69