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A tetrahedral ring is a term given in this work to a set of n regular tetrahedra joined face-to-face sharing a common edge (with internal conjoined faces removed). These ...

When the group order h of a finite group is a prime number, there is only one possible group of group order h. Furthermore, the group is cyclic.

A representation of a group G is a group action of G on a vector space V by invertible linear maps. For example, the group of two elements Z_2={0,1} has a representation phi ...

The kernel of a group homomorphism f:G-->G^' is the set of all elements of G which are mapped to the identity element of G^'. The kernel is a normal subgroup of G, and always ...

The double covering group of the (linear) symplectic group.

Given a commutative unit ring R, and an R-module M, a sequence {x_1,...,x_n} of elements of R is called a regular sequence for M (or an M-sequence for short), if, for all ...

Let R be a ring, and let I be an ideal of R. The correspondence A<->A/I is an inclusion preserving bijection between the set of subrings A of R that contain I and the set of ...

The set of all nonsingular affine transformations of a translation in space constitutes a group known as the affine group. The affine group contains the full linear group and ...

A continuous group G which has the topology of a T2-space is a topological group. The simplest example is the group of real numbers under addition. The homeomorphism group of ...

A von Neumann regular ring is a ring R such that for all a in R, there exists a b in R satisfying a=aba (Jacobson 1989, p. 196). More formally, a ring R is regular in the ...