Algebraic properties of elements

special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them

function that is its own inverse

thumb|On/Off buttons of a train's destination sign control panel. Pressing the On button (green) is an idempotent operation, since it has the same effect whether done once or multiple times. Likewise, pressing Off is idempotent. Idempotence (, ) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of places in abstract algebra (in particular, in the theory of projectors and closure operators) and functional programming (in whi

In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n such that x^n=0. The smallest such n is called the index of nilpotency or the degree of nilpotency of x.

in mathematics, an invertible element or a unit in a ring R

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special type of element of a set with respect to a binary composition operation on that set which, when composed with any element of the set, results in the absorbing element itself

element of an extension field which is a root of a non-zero polynomial with coefficients in the subfield

non-zero non-unit element in an integral domain that is not a product of two non-units

set of related mathematical properties