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- ...topological space]], we can associate various algebraic objects, such as [[group]]s and [[ring]]s. ...ps the simplest object of study in algebraic topology is the [[fundamental group]]. Let <math>X</math> be a [[path-connected]] topological space, and let <m3 KB (479 words) - 14:35, 1 December 2015
- ...oms of axiomatic quantum field theory, it would have to be trivial (i.e. a free field theory). However, the quantum Yang-Mills theory (no quarks) with a non-abelian gauge group is an exception. It has a property known as asymptotic freedom, meaning tha2 KB (363 words) - 14:31, 1 December 2015
- ...ory''' is the area of mathematics which deals directly with the study of [[group]]s. == Topics and results in group theory ==360 bytes (47 words) - 15:56, 20 May 2008
- A '''homogenous principal set''' is a type of [[group]] [[group action|action]] on a [[set]]. ...a group with a left operation on a set <math>S</math>. The <math>G</math>-group <math>S</math> is called a '''left homogeneous principal set under <math>G<3 KB (524 words) - 12:28, 21 February 2017
- ...ructures with [[identity]] elements. The construction can be applied to [[group]]s, [[ring]]s, and [[module]]s. ..., but in the case of [[group]]s, direct sum is normally used for [[abelian group]]s, since additive notation is usually used for a [[commutative]] operation2 KB (278 words) - 11:53, 6 June 2008
- ...s the simplest object of study in algebraic topology is the '''fundamental group'''. ...(a) = f(1-a)</math>). We call <math>\pi_1(X,x_0)</math> the '''fundamental group''' of <math>X</math>.8 KB (1,518 words) - 19:11, 23 January 2017