symmetric monoidal (∞,1)-category of spectra
A notion of ordered ring for strict orders which are not necessarily linear orders.
A strictly ordered ring is an ring $R$ with a strict order $\lt$ such that
$0 \lt 1$
for all $a \in R$ and $b \in R$, if $0 \lt a$ and $0 \lt b$, then $0 \lt a + b$
for all $a \in R$ and $b \in R$, if $0 \lt a$ and $0 \lt b$, then $0 \lt a \cdot b$
Every strictly ordered ring is a preordered ring given by the negation of the strict order. In the presence of excluded middle, every strictly ordered ring is a totally preordered ring.
Every linearly ordered ring is a strictly ordered ring.
Every ordered local ring is a strictly ordered ring where every element greater than zero or less than zero is invertible.
Every ordered Kock field is a example of a strictly ordered ring which in the presence of excluded middle is a linearly ordered ring.
Last revised on December 13, 2022 at 19:08:44. See the history of this page for a list of all contributions to it.