Magma (algebra)

Specifically, a magma consists of a set equipped with a single binary operation that must be closed by definition.

In a couple of reviews of subsequent papers in Zentralblatt, Brandt strongly disagreed with this overloading of terminology.

[3] According to Bergman and Hausknecht (1996): "There is no generally accepted word for a set with a not necessarily associative binary operation.

This morphism of magmas has been used in economics since 1863 when W. Stanley Jevons calculated the rate of inflation in 39 commodities in England in his A Serious Fall in the Value of Gold Ascertained, page 7.

The magma operation may be applied repeatedly, and in the general, non-associative case, the order matters, which is notated with parentheses.

The binary operation on MX is formed by wrapping each of the two operands in parentheses and juxtaposing them in the same order.

[9] It can also be viewed, in terms familiar in computer science, as the magma of full binary trees with leaves labelled by elements of X.

Commonly studied types of magma include: Note that each of divisibility and invertibility imply the cancellation property.