What is "unital"

a. (context mathematics English) (''of an algebra'') containing a multiplicative identity element (or unit), i.e. an element 1 with the property 1x = x1 = x for all elements x of the algebra.

Unital may refer to:

• A unital algebra – an algebra that contains a multiplicative identity element.
• A geometric unital – a block design for integer .
• A unital algebraic structure, such as a unital magma.
• A unital map on C*-algebras – a map that preserves the identity element.

In geometry, a unital is a set of n + 1 points arranged into subsets of size n + 1 so that every pair of distinct points of the set are contained in exactly one subset. n ≥ 3 is required by some authors to avoid small exceptional cases. This is equivalent to saying that a unital is a 2-(n + 1, n + 1, 1) block design. Some unitals may be embedded in a projective plane of order n (the subsets of the design become sets of collinear points in the projective plane). In this case of embedded unitals, every line of the plane intersects the unital in either 1 or n + 1 points. In the Desarguesian planes, PG(2,q), the classical examples of unitals are given by nondegenerate Hermitian curves. There are also many non-classical examples. The first and the only known unital with non prime power parameters, n=6, was constructed by Bhaskar Bagchi and Sunanda Bagchi. It is still unknown if this unital can be embedded in a projective plane of order 36, if such a plane exists.