In abstract algebra, a multiplicatively closed set (or multiplicative set) is a subset S of a ring R such that the following two conditions hold: 1 ∈ S...

commonly done with respect to a multiplicatively closed set S (also called a multiplicative set or a multiplicative system) of elements of a ring R,...

{\displaystyle S} be the set of elements that are not zero divisors in R {\displaystyle R} ; then S {\displaystyle S} is a multiplicatively closed set. Hence we may...

whole ring.) An ideal I is prime if and only if its set-theoretic complement is multiplicatively closed. Every nonzero ring contains at least one prime ideal...

follows that Tor commutes with localization. That is, for a multiplicatively closed set S in R, S − 1 Tor i R ⁡ ( A , B ) ≅ Tor i S − 1 R ⁡ ( S − 1 A...

Ext commutes with localization, in the sense that for every multiplicatively closed set S in R, every R-module B, and every integer i, S − 1 Ext R i...

is a Krull domain. If S ⊂ A {\displaystyle S\subset A} is a multiplicatively closed set not containing 0, the ring of quotients S − 1 A {\displaystyle...

Saturated measure, if every locally measurable set is also measurable Saturated multiplicatively closed sets, a concept in ring theory "Saturation (song)"...

In mathematics, an expression is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations...

256, ... (sequence A001013 in the OEIS) They form the smallest multiplicatively closed set containing all of the factorials. The n {\displaystyle n} th...