In principal ideal domains a near converse holds: every nonzero prime ideal is maximal.

In the category of sets the converse also holds, so the monomorphisms are exactly the injective morphisms.

The converse also holds in most naturally occurring categories of algebras because of the existence of a free object on one generator.

However, it also shows that the compactness of the product of compact Hausdorff spaces can be proved using ( BPIT ), and in fact the converse also holds.

The converse also holds: If the sum of the distances from a point in the interior of a quadrilateral to the sides is independent of the location of the point, then the quadrilateral is a parallelogram.

The converse also holds.

One can show that every prime element is irreducible ; the converse is not true in general but holds in unique factorization domains.

It is more interesting that the converse also holds: Every second countable T4 space is homeomorphic to a subset of the Hilbert cube.

He showed that the validity of such Horn formulas is preserved under nonempty direct products, and conjectured that the converse also holds.

The converse however is not true in general, but holds for graph with maximum degree not greater than three.

In fact, utilizing the holomorphic version of the Poincaré lemma, a partial converse holds true locally.

The converse also holds: for any solenoidal v there exists a vector potential A such that ( Strictly speaking, this holds only subject to certain technical conditions on v, see Helmholtz decomposition.

also showed that the converse holds on boards of size m × n provided m and n are both at least 2: all even permutations are solvable.

Some people call a formal group scheme smooth if the converse holds.

The converse also holds:

The converse holds in compression.

If f is flat and locally of finite presentation, then f is universally open .< ref > EGA IV < sub > 2 </ sub >, Théorème 2. 4. 6 .</ ref > However, if f is faithfully flat and quasi-compact, it is not in general true that f is open, even if X and Y are noetherian .< ref > EGA IV < sub > 2 </ sub >, Remarques 2. 4. 8 ( i ).</ ref > Furthermore, no converse to this statement holds: If f is the canonical map from the reduced scheme X < sub > red </ sub > to X, then f is a universal homeomorphism, but for X noetherian, f is never flat .< ref > EGA IV < sub > 2 </ sub >, Remarques 2. 4. 8 ( ii ).</ ref >

Also, a kind of converse holds: Every algebraic lattice is isomorphic to Sub ( A ) for some algebra A.

Here partial converse means that if M sums the series Σ, and some side-condition holds, then Σ was convergent in the first place ; without any side condition such a result would say that M only summed convergent series ( making it useless as a summation method for divergent series ).

In 1974 Harvey Friedman proved that in any recursively enumerable extension of intuitionistic arithmetic, the converse of the above also holds.

The converse statement also holds: any functor represented by a CW complex satisfies the above two properties.

The converse holds for bounded operators but fails in general.

* For Hausdorff spaces a cofibration is a closed inclusion ( injective with closed image ); for suitable spaces, a converse holds

Historian Michael Clanchy noted " the medieval axiom that laymen are illiterate and its converse that clergy are literate ", so it may be the case that few soldiers read Vegetius ' work.

Bargrave was brought before the city's chief inquisitor who suggested they converse in Latin rather than Italian so that the guards might be prevented from understanding them.

A non-vanishing p-minor ( p × p submatrix with non-vanishing determinant ) shows that the rows and columns of that submatrix are linearly independent, and thus those rows and columns of the full matrix are linearly independent ( in the full matrix ), so the row and column rank are at least as large as the determinantal rank ; however, the converse is less straightforward.

After connecting, the operator leaves both cords " up " with the keys in the normal position so the parties can converse.

In the converse, the given ( that two sides are equal ) and what is to be proved ( that two angles are equal ) are swapped, so the converse is the statement that if two angles of a triangle are equal then two sides are equal.

Th Diwan who was so charmed with his company that every evening he, with all the State officials, used to meet the Swami and converse with him until late at night.

Louis XVIII entered Paris on 8 July to a boisterous reception: the Tuileries Palace gardens were thronged with bystanders, and, according to the Duke of Wellington, the acclamation of the crowds there were so loud that evening, that he could not converse with the King.

The converse is also true: If points D, E and F are chosen on BC, AC and AB respectively so that

He casually gives the injured Mexican his spot on the travois as he perches himself backwards on the horse so the men can converse as they travel.

He liked the Chinese people so much that he learnt Mandarin in which language he could converse.

He was determined to bring men to Denmark to teach him and his people Latin so they could converse with the rest of Europe on equal terms.

Also, Goethe had died in March 1832, so he had less people to converse with at the Weimar theater.

A partial converse to this statement says that every representation of a finite-dimensional ( real or complex ) Lie algebra lifts to a unique representation of the associated simply connected Lie group, so that representations of simply-connected Lie groups are in one-to-one correspondence with representations of their Lie algebras.

: Your letter of yesterday is received & I hasten to answer as fully as I can -- Joseph Smith Jr first come to my notice in the year 1824 in the summer of that year I contracted with his father to build a fence on my property in the corse of that work I approach Joseph & ask how it is in a half day you put up what requires your father & 2 brothers a full day working together he says I have not been with out assistance but can not say more only you better find out the next day I take the older Smith by the arm & he says Joseph can see any thing he wishes by looking at a stone Joseph often sees Spirits here with great kettles of coin money it was Spirits who brought up rock because Joseph made no attempt on their money I latter dream I converse with spirits which let me count their money when I awake I have in my hand a dollar coin which I take for a sign Joseph describes what I seen in every particular says he the spirits are grieved so I through back the dollar in the fall of the year 1827 I hear Joseph found a gold bible I take Joseph aside & he says it is true I found it 4 years ago with my stone but only just got it because of the enchantment the old spirit come to me 3 times in the same dream & says dig up the gold but when I take it up the next morning the spirit transfigured himself from a white salamander in the bottom of the hole & struck me 3 times & held the treasure & would not let me have it because I lay it down to cover over the hole when the spirit says do not lay it down Joseph says when can I have it the spirit says one year from to day if you obay me look to the stone after a few days he looks the spirit says bring your brother Alvin Joseph says he is dead shall I bring what remains but the spirit is gone Joseph goes to get the gold bible but the spirit says you did not bring your brother you can not have it look to the stone Joseph looks but can not see who to bring the spirit says I tricked you again look to the stone Joseph looks & sees his wife on the 22d day of Sept 1827 they get the gold bible -- I give Joseph $ 50 to move him down to Pa Joseph says when you visit me I will give you a sign he gives me some hiroglyphics I take then to Utica Albany & New York in the last place Dr Mitchel gives me an introduction to Professor Anthon says he they are short hand Egyption the same what was used in ancient times bring me the old book & I will translate says I it is made of precious gold & is sealed from view says he I can not read a sealed book -- Joseph found some giant silver specticles with the plates he puts them in an old hat & in the darkness reads the words & in this way it is all translated & written down -- about the middle of June 1829 Joseph takes me together with Oliver Cowdery & David Whitmer to have a view of the plates our names are appended to the book of Mormon which I had printed with my own money -- space and time both prevent me from writing more at present if there is any thing further you wish to inquire I shall attend to it

After Sandwich was named as First Lord of the Admiralty, Rochford ’ s successor as northern secretary was Lord Suffolk, who spent a year improving his French so that he could converse with the foreign diplomats in London.

JCSP allows its channels to be buffered so can easily emulate the actor model ; the converse is not true.

The verification tone is added so that telephone subscribers will not be able to easily use the ringback system as an " intercom ," to call other extensions of their own phone line by simply initiating a ringback test and waiting for the phone to stop ringing and converse when someone has answered the extension.

He has the ability to resurrect the dead and converse with them, though to do so he must either have the complete corpse or its " essential saltes ," since incomplete bodies only yield incoherent abominations.

He says, " Um .. Would it be possible for you to tell me if there's Samantha Baker there and if so may I converse with her briefly?

The quote from Isaiah comes from a section about how all who obey God's will, Jewish or not, are to be allowed into the Temple so they can pray and therefore converse with God.

In fact, to compute Tor ( A, B ), one may use a flat resolution of A or B, instead of a projective resolution ( note that a projective resolution is automatically a flat resolution, but the converse isn't true, so allowing flat resolutions is more flexible ).

With video interpreting, sign language interpreters work remotely with live video and audio feeds, so that the interpreter can see the deaf or mute party, converse with the hearing party and vice versa.