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Given a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the associated graded ring of R with respect to F is the ...

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 ...

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 ...

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 ...

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 ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

An irreducible representation of a group is a group representation that has no nontrivial invariant subspaces. For example, the orthogonal group O(n) has an irreducible ...

A Lie algebra is a vector space g with a Lie bracket [X,Y], satisfying the Jacobi identity. Hence any element X gives a linear transformation given by ad(X)(Y)=[X,Y], (1) ...

A representation phi of a group G is faithful if it is one-to-one, i.e., if phi(g)=phi(h) implies g=h for g,h in G. Equivalently, phi is faithful if phi(g)=I_n implies g=e, ...