unital

Adjective

Meaning

unital (not comparable)

(mathematics) (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.

Synonyms

Phrases with the word

Anagrams

Examples

Example The 2 2-matrices over the reals form a unital algebra in the obvious way. Source: Internet

Formal definitions In a unital magma Let be a set closed under a binary operation (i. Source: Internet

If rings are not required to be unital, the last condition is omitted. Source: Internet

In a unital alternative algebra, multiplicative inverses are unique whenever they exist. Source: Internet

In fact the converse is also true and this gives a characterization of division rings via their module category: A unital ring R is a division ring if and only if every R- module is free Grillet, Pierre Antoine. Source: Internet

In other words, in a monoid (an associative unital magma) every element has at most one inverse (as defined in this section). Source: Internet

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