Null semigroup

In mathematics, a null semigroup (also called a zero semigroup) is a semigroup with an absorbing element, called zero, in which the product of any two elements is zero. If every element of the semigroup is a left zero then the semigroup is called a left zero semigroup; a right zero semigroup is defined analogously. According to Clifford and Preston, "In spite of their triviality, these semigroups arise naturally in a number of investigations."

Null semigroup

Let S be a semigroup with zero element 0. Then S is called a null semigroup if for all x and y in S we have xy = 0.

Cayley table for a null semigroup

Let S = { 0, a, b, c } be a null semigroup. Then the Cayley table for S is as given below:

Left zero semigroup

A semigroup in which every element is a left zero element is called a left zero semigroup. Thus a semigroup S is a left zero semigroup if for all x and y in S we have xy = x.

Cayley table for a left zero semigroup

Let S = { a, b, c } be a left zero semigroup. Then the Cayley table for S is as given below:

.mr

.mr is the Internet country code top-level domain (ccTLD) for Mauritania. A local contact is required to register a domain name under .mr. Registrations are taken directly at the second level, but a .gov.mr second level domain exists in which governmental sites can be found at the third level.

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Mr.

Mister, usually written in its abbreviated form Mr. (US) or Mr (US & UK), is a commonly-used English honorific for men under the rank of knighthood. The title derived from earlier forms of master, as the equivalent female titles Mrs, Miss, and Ms all derived from earlier forms of mistress. Master is sometimes still used as an honorific for boys and young men, but its use is increasingly uncommon.

The modern plural form is Misters, although its usual formal abbreviation Messrs(.) derives from use of the French title messieurs in the 18th century.Messieurs is the plural of monsieur (originally mon sieur, "my lord"), formed by declining both of its constituent parts separately.

Historic etiquette

Historically, mister—like Sir or my lord—was applied only to those above one's own status in the peerage. This understanding is now obsolete, as it was gradually expanded as a mark of respect to those of equal status and then to all gentlemen. It is now used indiscriminately.

In past centuries, Mr was used with a first name to distinguish among family members who might otherwise be confused in conversation: Mr Doe would be the eldest present; younger brothers or cousins were then referred to as Mr Richard Doe and Mr William Doe and so on. Such usage survived longer in family-owned business or when domestic servants were referring to adult male family members with the same surname: "Mr Robert and Mr Richard will be out this evening, but Mr Edward is dining in," but such usage today is rare in American culture but still quite common in others as a sign of respect when first names are being used, the last name is not known, or where English is not the mother tongue.

Mr. (band)

Mister also known as Mr. is a Hong Kong, Chinese rock band composed of lead vocalist Alan Po, rhythm guitarist Ronny Lay, lead guitarist Quincy Tam, bassist and backing vocalist Desmond Tam, and drummer Tom To.

The quintet originated from the underground indie scene where they were known as White Noise. Their breakthrough performance was their gig at Alan Tam's birthday party. They were subsequently recommended to Universal Music by himself who was deeply impressed by their skill and talent.

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