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Page "Principal ideal domain" ¶ 27
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# and Every
# Every adiabat asymptotically approaches both the V axis and the P axis ( just like isotherms ).
# Every net on X has a convergent subnet ( see the article on nets for a proof ).
# Every filter on X has a convergent refinement.
# Every ultrafilter on X converges to at least one point.
# Every infinite subset of X has a complete accumulation point.
# Every open cover of A has a finite subcover.
# Every sequence in A has a convergent subsequence, whose limit lies in A.
# Every infinite subset of A has at least one limit point in A.
# Every finite and contingent being has a cause.
# Every type of state is a powerful institution of the ruling class ; the state is an instrument which one class uses to secure its rule and enforce its preferred production relations ( and its exploitation ) onto society.
# " Personality " Argument: this argument is based on a quote from Hegel: " Every man has the right to turn his will upon a thing or make the thing an object of his will, that is to say, to set aside the mere thing and recreate it as his own ".
# Moral law of karma: Every action ( by way of body, speech, and mind ) will have karmic results ( a. k. a. reaction ).
# Every principal ideal domain is Noetherian.
# 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 possible answer takes the same amount of time to check, and
Good Trouble ( 1982 ) and Wheels Are Turnin ' ( 1984 ) were follow-up albums which also did well commercially, the former containing the hit singles " Keep the Fire Burnin '" ( U. S. # 7 ), " Sweet Time " ( U. S. # 26 ) and the un-ranked " The Key " and the latter containing the # 1 hit single " Can't Fight This Feeling " plus three more hits: " I Do ' Wanna Know " ( U. S. # 29 ), " One Lonely Night " ( U. S. # 19 ), " Live Every Moment " ( U. S. # 34 ) and the un-ranked " Break His Spell ".
# Every simple path from a given node to any of its descendant leaves contains the same number of black nodes.
# Every good work of software starts by scratching a developer's personal itch.
# Every noun belongs to a unique number class.

# and prime
# Install the assembly into the pump and prime the tubing ( this pushes insulin and any air bubbles through the tubing ).
# Attach to the infusion site to a body ( and prime the cannula to see if a new set has been inserted correctly )
St. Laurent was ranked # 4 on a survey of the first 20 prime ministers ( through Jean Chrétien ) of Canada done by Canadian historians, and used by J. L. Granatstein and Norman Hillmer in their book Prime Ministers: Ranking Canada's Leaders.
# If a and p are natural numbers such that a < sup > p </ sup > − 1 is prime, then a
# If 2 < sup > p </ sup >-1 is prime, then p is prime.
# If p is an odd prime, then any prime q that divides 2 < sup > p </ sup > − 1 must be 1 plus a multiple of 2p.
# If p is an odd prime, then any prime q that divides must be congruent to ± 1 ( mod 8 ).
# A Mersenne prime cannot be a Wieferich prime.
# In all unital rings, maximal ideals are prime.
# Choose two distinct prime numbers p and q.
# Receive one prime factor, F, of N from the future on channel c.
# Test that F ≠ N, that F divides N ( time complexity O ( log N )), and that F is prime ( polynomial time ; see AKS primality test ).
# The channel that is designated as a prime transmission channel and is used as the first choice in restoring priority circuits.
# Although technology might be a prime element in many public issues, nontechnical factors take precedence in technology-policy decisions.
# REDIRECT Twin prime
# redirect Twin prime # First Hardy – Littlewood conjecture
# redirect Boolean prime ideal theorem
# REDIRECT integral domain # Divisibility, prime elements, and irreducible elements

# and ideal
# While ideal gas molecules do not interact, we consider molecules attracting others within a distance of several molecules ' radii.
# Inertial reference systems, where the coordinate axes retain their orientation relative to the fixed stars, or equivalently, to the rotation axes of ideal gyroscopes ; the axis points to the vernal equinox
AA # 9, however, will fill the case much better, and the slow burn rate of AA # 9 is ideal for magnum handgun rounds, producing 20 % higher velocities ( at maximum levels ) while still producing less pressure than the fast burning AA # 2.
# All principal ideal domains are integrally closed.
# If n = 2k + 1, then the action of the unit vector u on the left ideal decomposes the space into a pair of isomorphic irreducible eigenspaces ( both denoted by Δ ), corresponding to the respective eigenvalues + 1 and − 1.
# Harmonic distortion: defined as a departure from the ideal sinusoidal waveform expected on the line.
# It is an ideal emitter: it emits as much or more energy at every frequency than any other body at the same temperature.
This is similar ( but more categorical ) to concepts in group theory or module theory, where a given decomposition of an object into a direct sum is " not natural ", or rather " not unique ", as automorphisms exist that do not preserve the direct sum decomposition – see Structure theorem for finitely generated modules over a principal ideal domain # Uniqueness for example.
# REDIRECT ideal ( ring theory )
# REDIRECT ideal ( ring theory )
# Methods: the most appropriate ways to achieve the ideal arrangement.
# In the Aeneid by Virgil, Nisus and Euryalus are ideal friends and lovers, who died during a raid on the Rutulians.
# those who, like Plato, distinguished ideal and mathematical numbers ;
# those who, like Xenocrates, identified ideal numbers with mathematical numbers
# SGI, based on the ideal of world citizenship, shall safeguard fundamental human rights and not discriminate against any individual on any grounds.
# SGI shall promote, based on the Buddhist ideal of symbiosis, the protection of nature and the environment.
# The ideal Social-Democratic welfare state is based on the principle of universalism granting access to benefits and services based on citizenship.
# Determine the target market's preferred combination of attributes ( referred to as an ideal vector )
# The radical of the ideal 4Z of integer multiples of 4 is 2Z.

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