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The primitive part of a polynomial P(x) is P(x)/k, where k is the content. For a general univariate polynomial P(x), the Wolfram Language function FactorTermsList[poly, x] ...

A specification of elements in a list as a list of pairs giving the element and number of times it occurs in a run. For example, given the list ...

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 ...

When a Young tableau is constructed using the so-called insertion algorithm, an element starts in some position on the first row, from which it may later be bumped. In ...

A group G is said to act on a set X when there is a map phi:G×X->X such that the following conditions hold for all elements x in X. 1. phi(e,x)=x where e is the identity ...

A free idempotent monoid is a monoid that satisfies the identity x^2=x and is generated by a set of elements. If the generating set of such a monoid is finite, then so is the ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...

An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication ...

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...

A topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. For the real numbers, the set of all open ...