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# E-dense semigroup

In abstract algebra, an E-dense semigroup (also called an E-inversive semigroup) is a semigroup in which every element a has at least one weak inverse x, meaning that xax. [1]

## Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

## Dense set

In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A &mdash; for instance, every real number is either a rational number or has one arbitrarily close to it (see Diophantine approximation).

## E-semigroup

In the area of mathematics known as semigroup theory, an E-semigroup is a semigroup in which the idempotents form a subsemigroup.

## Idempotence

Idempotence is the property of certain operations in mathematics and computer science, that can be applied multiple times without changing the result beyond the initial application.

## Krohn–Rhodes theory

In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components.

## Monogenic semigroup

In mathematics, a monogenic semigroup is a semigroup generated by a set containing only a single element.

## Regular semigroup

In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a, there exists an element x such that axa.

## Semigroup

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.

## Special classes of semigroups

In mathematics, a semigroup is a nonempty set together with an associative binary operation.

## Weak inverse

In mathematics, the term weak inverse is used with several meanings.

## References

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