THE CONNECTION BETWEEN LEFT PRUFER RING AND RIGHT PRUFER RING
Let R be a prime Goldie ring with non-zero identity. A ring R is called a right Prufer ring if the multiplication of each finitely generated right ideal of R with its inverse on the right side is equal to R and the multiplication on the left side of its inverse is equal to the right order of ideal,...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/22862 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let R be a prime Goldie ring with non-zero identity. A ring R is called a right Prufer ring if the multiplication of each finitely generated right ideal of R with its inverse on the right side is equal to R and the multiplication on the left side of its inverse is equal to the right order of ideal, for left Prufer ring is defined in similar way. This thesis deals with the characterization of Prufer ring through the concept of projective generator. A prime Goldie ring R is a right (left) Prufer ring if and only if every finitely generated right (left) R-ideal of R is a projective generator of right (left) R module over R. Furthermore, in this thesis, it was shown that a prime Goldie ring is left Prufer ring if and only if it is a right Prufer ring. |
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