| Summary: | Semigroup is a structure with a associative binary operation. Since
semigroup may not have an identity element and invers element, there is a
regularity characteristic of element in semigroup. If all of the element of
semigroup have regularity, then this semigroup is called regular semigroup.
�-regular semigroup is one of the class regular semigroups. It is a pair of
regular semigroup with the set of idempotent elements which satifies some
axioms. If the first axiom in the definition of �-regular semigroup which
explained about commutative law for idempotent elements leaving out, then a new
class of regular semigroup is defined, called p-regular semigroup. In this case, the
set of all �-regular semigroups is subset of the set of all p-regular semigroup.
After observing the characteristic of p-regular semigroup, define a
maximum idempotent-separating congruence in p-regular semigroup. This
congruence is the same congruence in the pair of orthodox and band. Finally
conclusion, p-regular semigroup is a generalized regular semigroup (orthodox)
which has the maximum idempotent-separating congruences.
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