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An alternating permutation is an arrangement of the elements c_1, ..., c_n such that no element c_i has a magnitude between c_(i-1) and c_(i+1) is called an alternating (or ...

Let A be a unital C^*-algebra, then an element u in A is called an isometry if u^*u=1.

A letter is an element of an alphabet. A collection of letters forms a word.

An element B of a ring is nilpotent if there exists a positive integer k for which B^k=0.

Let A be a C^*-algebra, then an element a in A is called normal if aa^*=a^*a.

Let A be a C^*-algebra, then an element u in A is called a partial isometry if uu^*u=u.

A unit in a ring is an element u such that there exists u^(-1) where u·u^(-1)=1.

A ring in the mathematical sense is a set S together with two binary operators + and * (commonly interpreted as addition and multiplication, respectively) satisfying the ...

A cycle of a finite group G is a minimal set of elements {A^0,A^1,...,A^n} such that A^0=A^n=I, where I is the identity element. A diagram of a group showing every cycle in ...

A cycle graph of a group is a graph which shows cycles of a group as well as the connectivity between the cycles. Such graphs are constructed by drawing labeled nodes, one ...