1 dividing an animal into right and left halves [syn: median]
2 relating to or situated in or extending toward the middle [syn: median]
- Of or pertaining to a mean or average; mean
- medial alligation
- pertaining to the inside (the part facing the body); for example, the medial side of the knee faces the other knee, while the outer side of the knee is lateral.
of or pertaining to a mean or average
- Finnish: keski-
pertaining to the inside
- Finnish: mediaalinen, sisäpuolinen
- This article is about medial in mathematics. For other uses, see medial (disambiguation).
- (x \cdot y) \cdot (u \cdot z) = (x \cdot u) \cdot (y \cdot z), or more simply, xy\cdot uz = xu\cdot yz
using the convention that juxtaposition has higher precedence. This identity has been variously called medial, abelian, alternation, transposition, bi-commutative, bisymmetric, surcommutative, entropic, etc.
Any commutative semigroup is a medial magma, and a medial magma has an identity element if and only if it is a commutative monoid. An elementary example of a nonassociative medial quasigroup can be constructed as follows: take an abelian group except the group of order 2 (written additively) and define a new operation by x * y = (− x) + (− y).
A magma M is medial if and only if its binary operation is a homomorphism from the Cartesian square M x M to M. This can easily be expressed in terms of a commutative diagram, and thus leads to the notion of a medial magma object in a category with a cartesian product. (See the discussion in auto magma object.)
If f and g are endomorphisms of a medial magma, then the mapping f.g defined by pointwise multiplication
- (f\cdot g)(x) = f(x)\cdot g(x)
is itself an endomorphism.
medial in Spanish: Medial (álgebra)
amidships, average, banal, center, centermost, central, common, core, equatorial, equidistant, fair, fairish, halfway, indifferent, intercurrent, interior, interjacent, intermediary, intermediate, intervenient, intervening, mean, median, mediocre, mediterranean, medium, mesial, mesne, mezzo, mid, middle, middle-of-the-road, middlemost, middling, midland, midmost, midships, midway, moderate, normal, nuclear, ordinary, routine, standard, usual