Left and right (algebra)
In algebra, the terms left and right denote the order of a binary operation (usually, but not always called "multiplication") in non-commutative algebraic structures. A binary operation ∗ is usually written in the infix form:
The argument s is placed on the left side, and the argument t is on the right side. Even if the symbol of the operation is omitted, the order of s and t does matter unless ∗ is commutative.
A two-sided property is fulfilled on both sides. A one-sided property is related to one (unspecified) of two sides.
Although terms are similar, left–right distinction in algebraic parlance is not related either to left and right limits in calculus, or to left and right in geometry.
A binary operation ∗ may be considered as a family of unary operators through currying
depending on t as a parameter. It is the family of right operations. Similarly,
defines the family of left operations parametrized with s.
If for some e, the left operation Le is identical, then e is called a left identity. Similarly, if Re = id, then e is a right identity.
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