Ad
related to: algebra makes no sense of work quote word template list of elements freeeducation.com has been visited by 100K+ users in the past month
- Education.com Blog
See what's new on Education.com,
explore classroom ideas, & more.
- Digital Games
Turn study time into an adventure
with fun challenges & characters.
- Educational Songs
Explore catchy, kid-friendly tunes
to get your kids excited to learn.
- Activities & Crafts
Stay creative & active with indoor
& outdoor activities for kids.
- Education.com Blog
Search results
Results from the WOW.Com Content Network
In mathematics, the idea of a free object is one of the basic concepts of abstract algebra.Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.
Over a field, the free algebra on n indeterminates can be constructed as the tensor algebra on an n-dimensional vector space. For a more general coefficient ring, the same construction works if we take the free module on n generators. The construction of the free algebra on E is functorial in nature and satisfies an appropriate universal property.
The free group F S with free generating set S can be constructed as follows. S is a set of symbols, and we suppose for every s in S there is a corresponding "inverse" symbol, s −1, in a set S −1. Let T = S ∪ S −1, and define a word in S to be any written product of elements of T. That is, a word in S is an element of the monoid ...
The term "algebra" is sometimes used in a more narrow sense to refer only to elementary algebra or only to abstract algebra. [14] When used as a countable noun , an algebra is a specific type of algebraic structure that involves a vector space equipped with a certain type of binary operation . [ 15 ]
The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing. Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference ...
This example yields a Boolean algebra with 16 elements; in general, for finite n, the free Boolean algebra with n generators has 2 n atoms, and therefore elements. If there are infinitely many generators, a similar situation prevails except that now there are no atoms.
A function (which in mathematics is generally defined as mapping the elements of one set A to elements of another B) is called "A onto B" (instead of "A to B" or "A into B") only if it is surjective; it may even be said that "f is onto" (i. e. surjective). Not translatable (without circumlocutions) to some languages other than English.
In mathematics, many types of algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures may be viewed in different ways, however the common starting point of algebra texts is that an algebraic object incorporates one or more sets with one or more binary operations or unary operations satisfying a ...
Ad
related to: algebra makes no sense of work quote word template list of elements freeeducation.com has been visited by 100K+ users in the past month