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composite field (Definition)

Let $ \{K_\alpha\}$, $ \alpha \in J$, be a collection of subfields of a field $ L$. The composite field of the collection is the smallest subfield of $ L$ that contains all the fields $ K_\alpha$.

The notation $ K_1 K_2$ (resp., $ K_1 K_2 \dots K_n$) is often used to denote the composite field of two (resp., finitely many) fields.



"composite field" is owned by djao.
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Other names:  compositum, composite extension

Attachments:
the compositum of a Galois extension and another extension is Galois (Theorem) by alozano
Galois group of the compositum of two Galois extensions (Theorem) by alozano
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Cross-references: contains, field, subfields, collection
There are 11 references to this entry.

This is version 2 of composite field, born on 2002-01-21, modified 2002-04-11.
Object id is 1511, canonical name is CompositeField.
Accessed 4617 times total.

Classification:
AMS MSC: 12F99 (Field theory and polynomials :: Field extensions :: Miscellaneous)
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