symmetric monoidal (∞,1)-category of spectra
For $R$ a commutative ring, a subset $S \hookrightarrow R$ of its set of elements is called multiplicative if it is closed under multiplication “$\cdot$”in $R$, hence if $s_1,s_2 \in S \hookrightarrow R$ implies that $s_1 \cdot s_2 \in S \hookrightarrow R$, or equivalently, that $S$ forms a subsemigroup of $R$. Usually one also demands that the unit element is in the set $S$, or equivalently, that $S$ forms a submonoid of $R$.
Every two-sided filter of a ring in a commutative ring is a multiplicative subset.
The localization of a commutative ring at a multiplicative subset exists, denoted $S^{-1}R$ or $R[S^{-1}]$.
Last revised on July 3, 2022 at 18:35:59. See the history of this page for a list of all contributions to it.