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E-dense semigroup

Index 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]

11 relations: Abstract algebra, Dense set, E-semigroup, Idempotence, Krohn–Rhodes theory, Monogenic semigroup, Regular semigroup, Semigroup, Semigroup Forum, Special classes of semigroups, Weak inverse.

Abstract algebra

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

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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, that is the closure of A is constituting the whole set X. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).

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

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

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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.

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Monogenic semigroup

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

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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.

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

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Semigroup Forum

Semigroup Forum (print, electronic) is a mathematics research journal published by Springer.

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Special classes of semigroups

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

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Weak inverse

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

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Redirects here:

0-inversive semigroup, E*-dense semigroup, E-inversive semigroup.


[1] https://en.wikipedia.org/wiki/E-dense_semigroup

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