Linearly disjoint

In mathematics, algebras A, B over a field k inside some field extension $\Omega$ of k (e.g., universal field) are said to be linearly disjoint over k if the following equivalent conditions are met:

Note that, since every subalgebra of $\Omega$ is a domain, (i) implies $A \otimes_k B$ is a domain (in particular reduced).

单词	Linearly disjoint
释义	Linearly disjoint 英语百科 Linearly disjoint In mathematics, algebras A, B over a field k inside some field extension $\Omega$ of k (e.g., universal field) are said to be linearly disjoint over k if the following equivalent conditions are met: Note that, since every subalgebra of $\Omega$ is a domain, (i) implies $A \otimes_k B$ is a domain (in particular reduced).
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