* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.

Every instrumental group ( or section ) has a principal who is generally responsible for leading the group and playing orchestral solos.

# Every principal ideal domain is Noetherian.

# Every prime ideal of A is principal.

# Every finitely generated ideal of A is principal ( i. e., A is a Bézout domain ) and A satisfies the ascending chain condition on principal ideals.

Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by, where √ is called the radical sign or radix.

Every game in the main Zelda series has consisted of three principal areas: an overworld in which movement is multidirectional, allowing the player some degree of freedom of action ; areas of interaction with other characters ( merely caves or hidden rooms in the first game, but expanding to entire towns and cities in subsequent games ) in which the player gains special items or advice ; and dungeons, areas of labyrinthine layout, usually underground, comprising a wide range of difficult enemies, bosses, and items.

Every finitely generated ideal of a Boolean ring is principal ( indeed, ( x, y )=( x + y + xy )).

Every such regular cover is a principal G-bundle, where G = Aut ( p ) is considered as a discrete topological group.

Erdman distinguished herself as a principal dancer in Graham's company in solo roles such as the Ideal Spectator in Every Soul is a Circus, the Speaking Fate in Punch and the Judy and the One Who Speaks in Letter to the World, Graham's ode to the American poet, Emily Dickinson.

Every year around Easter, the town sponsors a major festival called Settimana Enologica — or Wine Week — where visitors can enjoy the principal wines produced in the area including the comparatively simple red table wine, Montefalco Rosso, the more complex DOCG red wines Sagrantino, for which the area is famous, and the Montefalco Sagrantino secco.

The carnival parade in February: Every year thousands of people come out to Julio Centeno Avenue, the principal artery road to watch the parade of costumes, live band, and fun.

In 1998 she was the principal actress of the popular Mexican situation comedy Una familia con Ángel, and in 2000 she participated in the soap opera Todo por amor ; also in 2000, she debuted as hostess of the morning program Cada Mañana ( Every Morning ), until she left the show for personal reasons on November 2003.

** Every unital ring other than the trivial ring contains a maximal ideal.

Every character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.

* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.

Every simple R-module is isomorphic to a quotient R / m where m is a maximal right ideal of R. By the above paragraph, any quotient R / m is a simple module.

* Krull's theorem ( 1929 ): Every ring with a multiplicative identity has a maximal ideal.

Every prime ideal P in a Boolean ring R is maximal: the quotient ring R / P is an integral domain and also a Boolean ring, so it is isomorphic to the field F < sub > 2 </ sub >, which shows the maximality of P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.

* Every left ideal I in R is finitely generated, i. e. there exist elements a < sub > 1 </ sub >, ..., a < sub > n </ sub > in I such that I = Ra < sub > 1 </ sub > + ... + Ra < sub > n </ sub >.

( DD1 ) Every nonzero proper ideal factors into primes.

( DD3 ) Every fractional ideal of is invertible.

Every field of either type can be realized as the field of fractions of a Dedekind domain in which every non-zero ideal is of finite index.

: Every Boolean algebra contains a prime ideal.

Every element of the Baer radical is nilpotent, so it is a nil ideal.

In Leedskalnin's own publication A Book in Every Home he implies his " Sweet Sixteen " was more an ideal than a reality.

* Every localization of R at a maximal ideal is a field

Every meal can be eaten without any cooking ; when circumstances permit, the ideal method of preparation is to cook the entrees in a pressure cooker, heated on the standard issue Coleman stove, or by simply boiling the rations in its package in water.

Every free spirit looked upon her as protectoress and ideal .... Marguerite was the embodiment of charity.

Every domain name appears in a zone served by one or more authoritative name servers.

Every domain name ends in a top-level or first-level domain label.

Every function symbol has an associated arity, indicating the number of elements in the domain mapped onto each element of range.

Every polynomial in can be factorized into polynomials that are irreducible over F. This factorization is unique up to permutation of the factors and the multiplication of the factors by nonzero constants from F ( because the ring of polynomials over a field is a unique factorization domain whose units are the nonzero constant polynomials ).

The Highland MP and antiquarian, Charles Fraser-Mackintosh, comments on late eighteenth century evictions in the area of Kingussie, in his second series of " Antiquarian Notes " ( Inverness 1897, pp 369 et seq, public domain ) as follows: " Mr James MacPherson of Ossianic fame, who acquired Phoiness, Etterish, and Invernahaven, began this wretched business and did it so thoroughly that not much remained for his successors ....... Every place James MacPherson acquired was cleared, and he also had a craze for changing and obliterating the old names ......

* Every constant function whose domain and codomain are the same is idempotent.

* Every Jacobi-like polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and has Q

* Every Laguerre-like polynomial sequence can have its domain shifted, scaled, and / or reflected so that its interval of orthogonality is, and has Q =

* Every Hermite-like polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and has Q

Every domain D can be embedded in an ω-complete domain completion ( called the ω-completion or simply the completion of D ) that is, in a precise sense, the smallest ω-complete domain containing D. The isolated elements of completion are precisely the isolated elements of D, but in general completion contains limit points that are not found in D. completion is uniquely determined up to isomorphism.

Every village, town and city can build a Wizard Tower, and the Wizard only has to be inside one Wizard Tower, the other towers will also increase his domain.

Every domain that supports the SMTP protocol for electronic mail is required by RFC 5321 and, as early as 1982, by RFC 822, to have the postmaster address.

Every domain may have a different timeline, adjusting events based on the domain's current time.

Every incoming email has an IP address that is difficult to forge, a bunch of domain names in the email headers, and a few more in the commands from the sender's SMTP server.

* Every concave function that is nonnegative on its domain is log-concave.

Every record has a unique identifier, which indicates the domain name of the original repository where the record was created.