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More formally, proposition B is a corollary of proposition A, if B can be readily deduced from A or is self-evident from its proof. In many cases, a corollary corresponds to a special case of a larger theorem, [4] which makes the theorem easier to use and apply, [5] even though its importance is generally considered to be secondary to that of ...
Nakayama's lemma: Let U be a finitely generated right module over a (unital) ring R. If U is a non-zero module, then U · J( R ) is a proper submodule of U . [ 17 ]
In mathematics, the Yoneda lemma is a fundamental result in category theory. [1] It is an abstract result on functors of the type morphisms into a fixed object . It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just one object and only isomorphisms).
In mathematics and other fields, [a] a lemma (pl.: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem " or an "auxiliary theorem".
Whether the snake lemma holds in the category of groups depends on the definition of cokernel. If f : A → B {\displaystyle f:A\to B} is a homomorphism of groups, the universal property of the cokernel is satisfied by the natural map B → B / N ( im f ) {\displaystyle B\to B/N(\operatorname {im} f)} , where N ( im f ) {\displaystyle N ...
Dolls have been unveiled in honour of Women’s History Month and Barbie’s birthday
In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges is even. For example, if there is a party of people who shake hands, the number of people who shake an odd number of other people's hands is even. [ 1 ]
Mattel has modeled Barbie dolls after trailblazing activists, athletes, and celebrities. Barbie's Inspiring Women series includes Ida B. Wells, Rosa Parks, and Frida Kahlo.