If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If a is idempotent in the ring R, then so is ; a and b are orthogonal.

* If a is idempotent in the ring R, then aRa is again a ring, with multiplicative identity a.

If M is an R module and is its ring of endomorphisms, then if and only if there is a unique idempotent e in E such that and.

If a is a central idempotent, then the corner ring is a ring with multiplicative identity a.

If a decomposition exists with each c < sub > i </ sub > a centrally primitive idempotent, then R is a direct sum of the corner rings c < sub > i </ sub > Rc < sub > i </ sub >, each of which is ring irreducible.

If both operations of the semiring are idempotent, then the semiring is called doubly idempotent.

* If e = e < sup > 2 </ sup > is an idempotent in the ring R, then Re is a projective left module over R.

( If f is such an idempotent endomorphism of M, then M is the direct sum of ker ( f ) and im ( f ).

If e is an idempotent in a Jordan algebra A ( e < sup > 2 </ sup >= e ) and R is the operation of multiplication by e, then

If in the third identity we take H = G, we get that the set of commutators is stable under any endomorphism of G. This is in fact a generalization of the second identity, since we can take f to be the conjugation automorphism.

If M is simple, then f is either the zero homomorphism or injective because the kernel of f is a submodule of M. If N is simple, then f is either the zero homomorphism or surjective because the image of f is a submodule of N. If M = N, then f is an endomorphism of M, and if M is simple, then the prior two statements imply that f is either the zero homomorphism or an isomorphism.

* If K is a field and we consider the K-vector space K < sup > n </ sup >, then the endomorphism ring of K < sup > n </ sup > which consists of all K-linear maps from K < sup > n </ sup > to K < sup > n </ sup >.

* If a module is simple, then its endomorphism ring is a division ring ( this is sometimes called Schur's lemma ).

If the module is an injective module, then indecomposability is equivalent to the endomorphism ring being a local ring.

If the module is Artinian, Noetherian, projective or injective, then the endomorphism ring has a unique maximal ideal, so that it is a local ring.

* If an R module is finitely generated and projective ( that is, a progenerator ), then the endomorphism ring of the module and R share all Morita invariant properties.

* If p = 0 in S for some prime number p, then the taking of pth powers induces an endomorphism of G < sub > a </ sub >, and the kernel is the group scheme α < sub > p </ sub >.

If M is indecomposable and has finite length, then every endomorphism of M is either bijective or nilpotent.

If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism of A to itself, which is a derivation over K. An algebra A equipped with a distinguished derivation d forms a differential algebra, and is itself a significant object of study in areas such as differential Galois theory.

* If M is a finitely generated R-module and ƒ: M → M is a surjective endomorphism, then ƒ is an isomorphism.

If p is congruent to 1 modulo 4, then the right hand side equals ω, so in this case the Frobenius endomorphism of Z /( p ) is the identity.

If you walk into the ring because it is fun to show your dog, he will feel it and give you a good performance!!

If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.

If A itself is commutative ( as a ring ) then it is called a commutative R-algebra.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

If a fighter is knocked down during the fight, determined by whether the boxer touches the canvas floor of the ring with any part of their body other than the feet as a result of the opponent's punch and not a slip, as determined by the referee, the referee begins counting until the fighter returns to his or her feet and can continue.

If a compression test does give a low figure, and it has been determined it is not due to intake valve closure / camshaft characteristics, then one can differentiate between the cause being valve / seat seal issues and ring seal by squirting engine oil into the spark plug orifice, in a quantity sufficient to disperse across the piston crown and the circumference of the top ring land, and thereby effect the mentioned seal.

If a second compression test is performed shortly thereafter, and the new reading is much higher, it would be the ring seal that is problematic, whereas if the compression test pressure observed remains low, it is a valve sealing ( or more rarely head gasket, or breakthrough piston or rarer still cylinder wall damage ) issue.

If A is a fixed element of a ring ℜ, the first additional relation can also be interpreted as a Leibniz rule for the map given by B ↦.

If the sheet contains regions where the number of atoms in a ring is different from six, while the total number of atoms remains the same, a topological defect has formed.

* If we think of as the ring of real numbers, then the direct product again consists of.

The best known example is the ring of quaternions H. If we allow only rational instead of real coefficients in the constructions of the quaternions, we obtain another division ring.

If R is a commutative ring, and a and b are in R, then an element d of R is called a common divisor of a and b if it divides both a and b ( that is, if there are elements x and y in R such that d · x = a and d · y = b ).

If R is a Euclidean domain in which euclidean division is given algorithmically ( as is the case for instance when R = F where F is a field, or when R is the ring of Gaussian integers ), then greatest common divisors can be computed using a form of the Euclidean algorithm based on the division procedure.

If the network is one-dimensional, and the chain of nodes is connected to form a circular loop, the resulting topology is known as a ring.

If is a left-( respectively right -) Noetherian ring, then the polynomial ring is also a left-( respectively right -) Noetherian ring.

If brass is used after this ring appears, it risks a crack, or worse, a complete head separation, which will leave the forward portion of the brass lodged in the chamber of the gun.

If the condition only holds for all singleton subsets of R, then the ring is a right Rickart ring.