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A local-ringed space which is locally isomorphic to an affine scheme.

If pi on V and pi^' on V^' are irreducible representations and E:V|->V^' is a linear map such that pi^'(g)E=Epi(g) for all g in and group G, then E=0 or E is invertible. ...

Given an ideal A, a semiprime ring is one for which A^n=0 implies A=0 for any positive n. Every prime ring is semiprime.

A semiring is a set together with two binary operators S(+,*) satisfying the following conditions: 1. Additive associativity: For all a,b,c in S, (a+b)+c=a+(b+c), 2. Additive ...

A polynomial with coefficients in a field is separable if its factors have distinct roots in some extension field.

The name for the set of integers modulo m, denoted Z/mZ. If m is a prime p, then the modulus is a finite field F_p=Z/pZ.

A nonzero ring S whose only (two-sided) ideals are S itself and zero. Every commutative simple ring is a field. Every simple ring is a prime ring.

A finite set of equations in the same unknowns of which the common solutions have to be determined. Solution of simultaneous equations in implemented in the Wolfram Language ...

The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

The geometry of the Lie group R semidirect product with R^2, where R acts on R^2 by (t,(x,y))->(e^tx,e^(-t)y).