Category:Fields of Quotients

From ProofWiki
Jump to navigation Jump to search

This category contains results about Fields of Quotients.
Definitions specific to this category can be found in Definitions/Fields of Quotients.

A field of quotients of $D$ is a pair $\struct {F, \iota}$ where:

$(1): \quad$ $F$ is a field
$(2): \quad$ $\iota : D \to F$ is a ring monomorphism
$(3): \quad \forall z \in F: \exists x \in D, y \in D_{\ne 0}: z = \dfrac {\map \iota x} {\map \iota y}$