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Let R be a ring, let A be a subring, and let B be an ideal of R. Then A+B={a+b:a in A,b in B} is a subring of R, A intersection B is an ideal of A and (A+B)/B=A/(A ...

An expression built up from statements letters by appropriate application of connectives (Mendelson 1997, p. 13).

A symbol used to represent a Boolean statement in logic that can take the value either true or false. All statement letters are statements forms (Mendelson 1997, p. 13).

A subring of a ring R is a subgroup of R that is closed under multiplication.

A subsequence of {a} is a sequence {b} defined by b_k=a_(n_k), where n_1<n_2<... is an increasing sequence of indices (D'Angelo and West 2000). For example, the prime numbers ...

Let R be a ring, and let I and J be ideals of R with I subset= J. Then J/I is an ideal of R/I and (R/I)/(J/I)=R/J.

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 ...

A relation on a totally ordered set.

A trail is a walk v_0, e_1, v_1, ..., v_k with no repeated edge. The length of a trail is its number of edges. A u,v-trail is a trail with first vertex u and last vertex v, ...

A one-sided (singly infinite) Laplace transform, L_t[f(t)](s)=int_0^inftyf(t)e^(-st)dt. This is the most common variety of Laplace transform and it what is usually meant by ...