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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 set is
Biordered_set
Property of operations
"open" button is not idempotent, because each press adds further delay. Biordered set Closure operator Fixed point (mathematics) Idempotent of a code Idempotent
Idempotence
Algebraic structure
have sometimes been considered by various authors. Absorbing element Biordered set Compact semigroup Empty semigroup Generalized inverse Identity element
Semigroup
Endofunction Semiautomaton Krohn–Rhodes theory Symmetric inverse semigroup Biordered set Special classes of semigroups Composition ring Dominique Perrin; Jean
Transformation_semigroup
hold. eventually regular semigroup E-dense (aka E-inversive) semigroup Biordered set Special classes of semigroups Nambooripad order Generalized inverse
Regular_semigroup
Indian mathematician (1935–2020)
of the set of idempotents in a regular semigroup. He called a set having this structure a biordered set. "The axioms defining a biordered set are quite
K._S._S._Nambooripad
Structure in group theory (in mathematics)
various applications in theoretical computer science. Orthodox semigroup Biordered set Pseudogroup Partial symmetries Regular semigroup Semilattice Green's
Inverse_semigroup
BIORDERED SET
BIORDERED SET
Boy/Male
Arabic, Australian, Muslim
Ordered; Appointed
Female
Japanese
(節å) Japanese name SETSUKO means "temperate child."
Girl/Female
African, Arabic, Muslim
Well-ordered; Well-arranged
Boy/Male
Muslim
Ordered, Pasted, Appointed
Boy/Male
Indian
Ordered, Pasted, Appointed
Male
English
Anglicized form of Hebrew Sheth, SETH means "buttocks." In the bible, this is the name of the third son of Adam and Eve. Compare with other forms of Seth.
Surname or Lastname
English
English : habitational name from a place in North Yorkshire, so named from Old English setl ‘seat’, ‘dwelling’.
Surname or Lastname
English
English : occupational name for a stone- or bricklayer, from Middle English setter ‘one who lays stones or bricks in building’ (agent derivative of setten ‘to set’).English : occupational name from Old French saietier ‘silk weaver’ (an agent derivative of sayete, a kind of silk).English : from an agent derivative of Middle English setten ‘to place (decoration, on a garment or metal surface)’, probably an occupational name for an embroiderer.German : unexplained.Norwegian : unexplained.
Male
Greek
(Σήθος) Greek form of Egyptian Sutekh, possibly SETHOS means "one who dazzles." In mythology, this is the name of an ancient evil god of Chaos, storms, and the desert, who slew Osiris.Â
Boy/Male
Indian
Responsibility; Ordered
Male
Italian
Italian form of Roman Latin Septimus, SETTIMIO means "seventh."
Male
Greek
(Σήθι) Greek form of Egyptian Seti, SETHI means "of Seth."Â
Girl/Female
Indian
Well-arranged, Well-ordered
Male
Greek
(ΑγÏίππας) Greek name AGRIPPAS means "wild horse." In the New Testament bible, this is the name of the Herod Agrippa who ordered the execution of the apostle James, and the imprisonment of Peter.
Girl/Female
Muslim
Well-arranged, Well-ordered
Boy/Male
Hindu, Indian, Telugu
Bordered; Friendly Element
Male
Greek
(ἩÏώδης) Greek name HERODES means "sprung from a hero." In the bible, this is the name of the king who ordered the slaughter of all male children "two years old and under."Â
Surname or Lastname
English
English : patronymic from Setter.
Boy/Male
African, Indian, Sanskrit
Clear Spoken Person; Ordered
Boy/Male
Tamil
Mitanshu | மீதாஂஷà¯Â
Bordered, Friendly element
BIORDERED SET
BIORDERED SET
Girl/Female
Tamil
Initiation
Female
English
 Pet form of English Adelaide, ADDIE means "noble sort." Compare with another form of Addie.
Boy/Male
Tamil
Girl/Female
American, British, English
Crowned with Laurels; Variant of Laura or Lora Referring to the Laurel Tree; Sweet Bay Tree Symbolic of Honor and Victory
Boy/Male
Indian
Lord
Male
English
Noble, Bright
Girl/Female
Muslim
Helpful
Girl/Female
Indian
Container of glory
Male
Croatian
, sound of peace.
Boy/Male
Sikh
Light of contentment
BIORDERED SET
BIORDERED SET
BIORDERED SET
BIORDERED SET
BIORDERED SET
a.
Disordered in the head; dizzy; delirious.
imp. & p. p.
of Broider
a.
Disordered.
a.
Thrown into disorder; deranged; as, a disordered house, judgment.
imp. & p. p.
of Border
a.
Disordered; disturbed.
a.
Disordered in the brain.
p.a.
Braided; broidered.
a.
Disorderly.
a.
Disordered or unsettled in intellect; deranged.
a.
Diseased; disordered.
imp. & p. p.
of Disorder
a.
Disordered; disturbed; disquieted.
p. p. & a.
Bordered by a beach.
superl.
Disordered in intellect; crazy; insane.
a.
Bordered with a distinct line of color.
a.
Disordered; especially, disordered in mind; crazy; insane.
a.
Disturbed; confused; disordered.
a.
Mentally disordered; unsettled; mad.
a.
Disordered in mind; hot-headed.