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A ring defined on a singleton set {*}. The ring operations (multiplication and addition) are defined in the only possible way, *·*=*, (1) and *+*=*. (2) It follows that this ...

The term two-sided ideal is used in noncommutative rings to denote a subset that is both a right ideal and a left ideal. In commutative rings, where right and left are ...

A unit matrix is an integer matrix consisting of all 1s. The m×n unit matrix is often denoted J_(mn), or J_n if m=n. Square unit matrices J_n have determinant 0 for n>=2. An ...

The notion of weak amenability was first introduced by Bade et al. (1987), who termed a commutative Banach algebra A "weakly amenable" if every continuous derivation from A ...

There are at least two theorems known as Weierstrass's theorem. The first states that the only hypercomplex number systems with commutative multiplication and addition are ...

There are at least two distinct notions known as the Whitehead group. Given an associative ring A with unit, the Whitehead group associated to A is the commutative quotient ...

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...

Pre-Algebra

An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...