Definitions for medialˈmi di əl
This page provides all possible meanings and translations of the word medial
dividing an animal into right and left halves
relating to or situated in or extending toward the middle
One or more letters that occur in the middle of a word.
Any of various things that occur in the middle.
Of or pertaining to a mean or average.
Pertaining to the inside; closer to the midline.
The medial side of the knee faces the other knee, while the outer side of the knee is lateral.
Origin: From medialis.
of or pertaining to a mean or average; mean; as, medial alligation
see 2d Media
Origin: [L. medialis, fr. medius middle: cf. F. mdial. See Middle.]
In abstract algebra, a medial magma is a set with a binary operation which satisfies the identity using the convention that juxtaposition denotes the same operation but has higher precedence. This identity has been variously called medial, abelian, alternation, transposition, interchange, 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. Another class of semigroups forming medial magmas are the normal bands. Medial magmas need not be associative: for any nontrivial abelian group and integers m ≠ n, replacing the group operation with the binary operation yields a medial magma which in general is neither associative nor commutative. Using the categorial definition of the product, one may define the Cartesian square magma M × M with the operation The binary operation ∙ of M, considered as a function on M × M, maps to x∙y, to u∙v, and to ∙ . Hence, a magma M is medial if and only if its binary operation is a magma homomorphism from M × 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.
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