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A short exact sequence of groups A, B, and C is given by two maps alpha:A->B and beta:B->C and is written 0->A->B->C->0. (1) Because it is an exact sequence, alpha is ...

The orthogonal complement of a subspace V of the vector space R^n is the set of vectors which are orthogonal to all elements of V. For example, the orthogonal complement of ...

An injective module is the dual notion to the projective module. A module M over a unit ring R is called injective iff whenever M is contained as a submodule in a module N, ...

In a set X equipped with a binary operation · called a product, the multiplicative identity is an element e such that e·x=x·e=x for all x in X. It can be, for example, the ...

Kontsevich's integral is a far-reaching generalization of the Gauss integral for the linking number, and provides a tool to construct the universal Vassiliev invariant of a ...

Cohomology is an invariant of a topological space, formally "dual" to homology, and so it detects "holes" in a space. Cohomology has more algebraic structure than homology, ...

The cubic groups are the point groups T_h and O_h together with their pure rotation subgroups T_d, T, and O (Cotton 1990, pp. 433-434).

A semigroup with a noncommutative product in which no product can ever be expressed more simply in terms of other elements.

Consider n strings, each oriented vertically from a lower to an upper "bar." If this is the least number of strings needed to make a closed braid representation of a link, n ...

There are seven frieze groups, which can be written in orbifold notation as *22infty, 2*infty, 22infty, *inftyinfty, infty*, inftyx, inftyinfty.