A binary map in a given group G, given by [g, h] = ghg−1h−1, where g and h are elements of G, which yields the group's identity if and only if the group operation commutes for g and h.
A binary map in a given ring R, given by [a, b] = ab − ba, where a and b are elements of R, which yields the ring's zeroelement if and only if the multiplication operation commutes for a and b.
Modern English dictionary
Explore and search massive catalog of over 900,000 word meanings.
Word of the Day
Get a curated memorable word every day.
Challenge yourself
Level up your vocabulary by setting personal goals.