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A nonzero and noninvertible element a of a ring R which generates a prime ideal. It can also be characterized by the condition that whenever a divides a product in R, a ...

A ring with a unit element in which every element is idempotent.

A group whose group operation is identified with multiplication. As with normal multiplication, the multiplication operation on group elements is either denoted by a raised ...

A set S together with a relation >= which is both transitive and reflexive such that for any two elements a,b in S, there exists another element c in S with c>=a and c>=b. In ...

The number of elements greater than i to the left of i in a permutation gives the ith element of the inversion vector (Skiena 1990, p. 27).

For a group G, consider a subgroup H with elements h_i and an element x of G not in H, then xh_i for i=1, 2, ... constitute the left coset of the subgroup H with respect to x.

Let H be a subgroup of G. A subset T of elements of G is called a left transversal of H if T contains exactly one element of each left coset of H.

The reflexive closure of a binary relation R on a set X is the minimal reflexive relation R^' on X that contains R. Thus aR^'a for every element a of X and aR^'b for distinct ...

Consider a countable subgroup H with elements h_i and an element x not in H, then h_ix for i=1, 2, ... constitute the right coset of the subgroup H with respect to x.

Let H be a subgroup of G. A subset T of elements of G is called a right transversal of H if T contains exactly one element of each right coset of H.