Multiplicatively Closed Set
In abstract algebra, a subset of a ring is said to be multiplicatively closed if it is closed under multiplication (i.e., xy is in the set when x and y are in it) and contains 1 but doesn't contain 0. The condition is especially important in commutative algebra, where multiplicatively closed sets are used to build localizations of commutative rings.
Read more about Multiplicatively Closed Set: Examples, Properties, See Also
Famous quotes containing the words closed and/or set:
“Don: Why are they closed? They’re all closed, every one of them.
Pawnbroker: Sure they are. It’s Yom Kippur.
Don: It’s what?
Pawnbroker: It’s Yom Kippur, a Jewish holiday.
Don: It is? So what about Kelly’s and Gallagher’s?
Pawnbroker: They’re closed, too. We’ve got an agreement. They keep closed on Yom Kippur and we don’t open on St. Patrick’s.”
—Billy Wilder (b. 1906)
“What shall we say who have knowledge
Carried to the heart? Shall we take the act
To the grave? Shall we, more hopeful, set up the grave
In the house? The ravenous grave?”
—Allen Tate (1899–1979)