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An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an ...

If x is a member of a set A, then x is said to be an element of A, written x in A. If x is not an element of A, this is written x not in A. The term element also refers to a ...

A ring in which the zero ideal is an irreducible ideal. Every integral domain R is irreducible since if I and J are two nonzero ideals of R, and a in I, b in J are nonzero ...

A proper ideal of a ring that is not the intersection of two ideals which properly contain it. In a principal ideal domain, the ideal I=<a> is irreducible iff a=0 or a is an ...

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 ...

The identity element I (also denoted E, e, or 1) of a group or related mathematical structure S is the unique element such that Ia=aI=a for every element a in S. The symbol ...

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

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

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

A function element is an ordered pair (f,U) where U is a disk D(Z_0,r) and f is an analytic function defined on U. If W is an open set, then a function element in W is a pair ...