In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such that axa = a.[1] Regular semigroups are one of the most-studied classes of semigroups, and their structure is particularly amenable to study via Green's relations.[2]
In mathematics, a regularsemigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such...
these we mention: regularsemigroups, orthodox semigroups, semigroups with involution, inverse semigroups and cancellative semigroups. There are also interesting...
mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism...
that x = xyx and y = yxy, i.e. a regularsemigroup in which every element has a unique inverse. Inverse semigroups appear in a range of contexts; for...
an I-semigroup and a *-semigroup. A class of semigroups important in semigroup theory are completely regularsemigroups; these are I-semigroups in which...
completely regularsemigroup is a semigroup in which every element is in some subgroup of the semigroup. The class of completely regularsemigroups forms an...
mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying...
Neumann regular ring, or absolutely flat ring (unrelated to the previous sense) Regular semi-algebraic systems in computer algebra Regularsemigroup, related...
In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is...
In algebra, a transformation semigroup (or composition semigroup) is a collection of transformations (functions from a set to itself) that is closed under...
mathematical structure that involves associative multiplication, that is, in a semigroup. This article describes generalized inverses of a matrix A {\displaystyle...
regular. A regularsemigroup is a semigroup in which every element is regular. This is a stronger notion than weak inverse. Every regularsemigroup is...
or occasionally as the full linear semigroup or general linear monoid. Notably, it constitutes a regularsemigroup. If one removes the restriction of...
published in 1979. Every catholic semigroup either is a regularsemigroup or has precisely one element that is not regular, much like the partitioners of...
orthodox semigroup is a regularsemigroup whose set of idempotents forms a subsemigroup. In more recent terminology, an orthodox semigroup is a regular E-semigroup...
Nambooripad's partial order) is a certain natural partial order on a regularsemigroup discovered by K S S Nambooripad in late seventies. Since the same...
inverse (called a pseudoinverse) because the symmetric semigroup is a regularsemigroup. If Y ⊆ X, then f: X→Y may compose with itself; this is sometimes...
{\displaystyle X,} forms a regularsemigroup called the semigroup of all partial transformations (or the partial transformation semigroup on X {\displaystyle...
a semigroup. The set of idempotents in a semigroup is a biordered set and every biordered set is the set of idempotents of some semigroup. A regular biordered...
and semigroups. It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup). The study of semigroups as images...
Rees matrix semigroups are a special class of semigroups introduced by David Rees in 1940. They are of fundamental importance in semigroup theory because...
In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating...
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