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Magma (algebra) — In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure. Specifically, a magma consists of a set M equipped with a single binary operation . A binary operation is… … Wikipedia
Alternativity — In abstract algebra, a magma G is said to be left alternative if ( xx ) y = x ( xy ) for all x and y in G and right alternative if y ( xx )=( yx ) x for all x and y in G . A magma that is both left and right alternative is said to be… … Wikipedia
Total quotient ring — In mathematics, the total quotient ring is a construction that generalizes the notion of the field of fractions of a domain to rings that may have zero divisors. The idea is to formally invert as many elements of the ring as possible without… … Wikipedia
Problems in loop theory and quasigroup theory — In mathematics, especially abstract algebra, loop theory and quasigroup theory are active research areas with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Many … Wikipedia

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