Definition:Quotient Field/Definition 2

From ProofWiki
Jump to navigation Jump to search


Let $D$ be an integral domain.

A quotient field of $D$ is a pair $\struct {F, \iota}$ such that:

$(1): \quad F$ is a field
$(2): \quad \iota: D \to F$ is a ring monomorphism
$(3): \quad$ If $K$ is a field with $\iota \sqbrk D \subset K \subset F$, then $K = F$.

That is, the quotient field of an integral domain $D$ is the smallest field containing $D$ as a subring.

Also see