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The Goldberg graphs are a family of graphs discovered by Goldberg (1981) which are snarks for n=5, 7, 9, .... Precomputed properties of Goldberg graphs are implemented in the ...

Let E and F be paired spaces with S a family of absolutely convex bounded sets of F such that the sets of S generate F and, if B_1,B_2 in S, then there exists a B_3 in S such ...

A group representation of a group G on a vector space V can be restricted to a subgroup H. For example, the symmetric group on three letters has a representation phi on R^2 ...

If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are ...

The gyroelongated pentagonal bicupola is the Johnson solid J_(46), which consists of two pentagonal cupolas, one twisted with respect to the other, adjoined to a decagonal ...

If R is a Noetherian ring, then S=R[X] is also a Noetherian ring.

Let K be an algebraically closed field and let I be an ideal in K(x), where x=(x_1,x_2,...,x_n) is a finite set of indeterminates. Let p in K(x) be such that for any ...

A function which is not defined explicitly, but rather is defined in terms of an algebraic relationship (which can not, in general, be "solved" for the function in question). ...

The integral closure of a commutative unit ring R in an extension ring S is the set of all elements of S which are integral over R. It is a subring of S containing R.

Given a commutative unit ring R and an extension ring S, an element s of S is called integral over R if it is one of the roots of a monic polynomial with coefficients in R.