Category:Prime Elements of Rings

From ProofWiki
Jump to navigation Jump to search

This category contains results about Prime Elements of Rings.
Definitions specific to this category can be found in Definitions/Prime Elements of Rings.

Let $R$ be a commutative ring.

Let $p \in R \setminus \set 0$ be any non-zero element of $R$.

Then $p$ is a prime element of $R$ if and only if:

$(1): \quad p$ is not a unit of $R$
$(2): \quad$ whenever $a, b \in R$ such that $p$ divides $a b$, then either $p$ divides $a$ or $p$ divides $b$.

Pages in category "Prime Elements of Rings"

This category contains only the following page.