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A group of five elements.

An Abelian category is a category for which the constructions and techniques of homological algebra are available. The basic examples of such categories are the category of ...

A knot that secures a rope to a post, ring, another rope, etc., but does not keep its shape by itself.

Let R be a commutative ring. A category C is called an R-category if the Hom-sets of C are R-modules.

A ring that is commutative under multiplication, has a multiplicative identity element, and has no divisors of 0. The integers form an integral domain.

An almost unit is a nonunit in the integral domain of formal power series with a nonzero first coefficient, P=a_1x+a_2x^2+..., where a_1!=0. Under the operation of ...

A subset of a topological group which is closed as a subset and also a subgroup.

A subgroup is a subset H of group elements of a group G that satisfies the four group requirements. It must therefore contain the identity element. "H is a subgroup of G" is ...

An anyon is a projective representation of a Lie group.

The tensor product between modules A and B is a more general notion than the vector space tensor product. In this case, we replace "scalars" by a ring R. The familiar ...