International Journal of Mathematics Trends and Technology
Volume 34 | Number 1 | Year 2016 | Article Id. IJMTT-V34P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V34P503
In mathematics a representation theorem is a theorem which states that each abstract structure with certain properties is isomorphic to a concrete structure. There are several examples of theorems of representation in various fields of mathematics: . In algebra, the theorem of Cayley states that each group is isomorphic to a group transformed a whole. The representation theory studies the properties of abstract groups through their representation as transformations of vector spaces. Additionally, also in algebra, Stone representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a field of sets. A variant of this theorem channeled reticles requires each distributive lattice is isomorphic to a reticle sub-lattice power set of a set. . In category theory, the Yoneda lemma explains how arbitrary functors in the category of sets can be seen as hom functions. . In set theory, the Mostowski collapsing theorem states that every well-founded extensional structure is isomorphic to a transitive set with the relation of belonging (∈). In functional analysis, the Riesz representation theorem is currently a list of many theorems. One identifies the dual space C0 (X) with the set of regular measurements in X.in geometry, the Whitney embedding theorems embed any abstract manifold in some Euclidean space. The Nash embedding theorem embeds an abstract Riemannian manifold isometrically in a Euclidean space. But the aim of this work is the algebraic applications, specially the representation theory.
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Sahar Jaafar Mahmood Abumalah, "A work on Representation Theorem’s and Algebraic Applications," International Journal of Mathematics Trends and Technology (IJMTT), vol. 34, no. 1, pp. 9-12, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V34P503
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