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abstrct: <br /> <br /> <br /> <br /> <br /> An algebra (A,.,+;k) over a field is a ring (A,.,+) endowed with an action of k on A which is compatible with both the multiplication and addition. Thus (A,.,+) is a ring, (A, +; k) is a vector space and myu(ab)=(myu a)b=...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/6023 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | abstrct: <br />
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An algebra (A,.,+;k) over a field is a ring (A,.,+) endowed with an action of k on A which is compatible with both the multiplication and addition. Thus (A,.,+) is a ring, (A, +; k) is a vector space and myu(ab)=(myu a)b=a(myu b) for all a, b equifalent A and myu equifalent k. Tensor product will suggest to the algebra definition equivalently with the first definition above. The duality of this definition suggests to the concept of a coalgebra. This thesis shows that any algebra is the dual of coalgebra and the convers is true if the algebra dimension is finite. |
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