Let the open enemy to it be regarded as a Pandora with her box opened ; ;

Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.

`` Let him be now ''!!

Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

Let Af be the null space of Af.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.

Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.

Let this be denoted by Af.

Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.

Let not your heart be troubled, neither let it be afraid ''.

The same God who called this world into being when He said: `` Let there be light ''!!

For those who put their trust in Him He still says every day again: `` Let there be light ''!!

Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.

Let her out, let her out -- that would be the solution, wouldn't it??

Let S be the group of all permutations of N, the natural numbers, that fixes all but finitely many numbers then:

Let R be a Noetherian ring and let I be an ideal of R. Then I may be written as the intersection of finitely many primary ideals with distinct radicals ; that is:

Let us briefly recall the structure theory in the case of a finitely generated module over a PID.

Let P be a finitely generated projective module over a commutative ring R and X be the spectrum of R. The rank of P at a prime ideal in X is the rank of the free-module.

Let k be a field and A finitely generated k-algebra.

Let A ⊆ R → S be homomorphisms where R is not necessarily local ( one can reduce to that case however ), with A, S regular and R finitely generated as an A-module.

Let G be a finitely generated nilpotent group with lower central series

Let G be a finitely generated group.

Let G be a finitely generated torsionfree nilpotent group.

Let k be a field and M a finitely generated module over the polynomial ring

* Let M be a finitely generated module over a local ring.

* Let R be a local ring and M a finitely generated module over R. Then the projective dimension of M over R is equal to the length of every minimal free resolution of M. Moreover, the projective dimension is equal to the global dimension of M, which is by definition the smallest integer i ≥ 0 such that

: Nakayama's lemma: Let U be a finitely generated right module over a ring R. If U is a non-zero module, then U · J ( R ) is a proper submodule of U.

Let ρ be the initial topology on X induced by C < sub > τ </ sub >( X ) or, equivalently, the topology generated by the basis of cozero sets in ( X, τ ).

Let vectors and let denote the matrix with elements of a and b. Then the area of the parallelogram generated by a and b is equal to.

Let vectors and let Then the area of the parallelogram generated by a and b is equal to.

Let A = < a > be the subgroup of Dic < sub > n </ sub > generated by a.

The 1967 musical Hair generated the same-named 1968 album, whose cuts include " Aquarius " and " Let The Sunshine In ", " Hair ", " Good Morning Starshine ", " Easy To Be Hard " ( covered, chronologically and respectively, by The 5th Dimension at # 1, The Cowsills at # 2, Oliver at # 3, Three Dog Night at # 4, on the Hot 100 in 1969 ), and others, and a London Cast album released in April 1969.

Let us consider only prompt neutrons, and let ν denote the number of prompt neutrons generated in a nuclear fission.

Let h *< sub > 0 </ sub > be the real subspace of h * ( if it is complex ) generated by the roots of g.

Let be any set, let be an algebraic structure of type generated by.

Let k be a field and L and K be two extensions of k. The compositum, denoted KL is defined to be where the right-hand side denotes the extension generated by K and L. Note that this assumes some field containing both K and L. Either one starts in a situation where such a common over-field is easy to identify ( for example if K and L are both subfields of the complex numbers ); or one proves a result that allows one to place both K and L ( as isomorphic copies ) in some large enough field.

Let p be a prime number and let K = Q ( μ < sub > p </ sub >) be the field generated over Q by the pth roots of unity.

Indeed, let K be an imaginary quadratic field with class field H. Let E be an elliptic curve with complex multiplication by the integers of K, defined over H. Then the maximal abelian extension of K is generated by the x-coordinates of the points of finite order on some Weierstrass model for E over H.

Let U be an open set in a manifold M, Ω < sup > 1 </ sup >( U ) be the space of smooth, differentiable 1-forms on U, and F be a submodule of Ω < sup > 1 </ sup >( U ) of rank r, the rank being constant in value over U. The Frobenius theorem states that F is integrable if and only if for every the stalk F < sub > p </ sub > is generated by r exact differential forms.

Let X < sup >*</ sup > be the set of all words in X ( i. e. the free monoid generated by X ).

Let Q ( μ ) be the cyclotomic extension of Q generated by μ, where μ is a primitive p < sup > th </ sup > root of unity ; the Galois group of Q ( μ )/ Q is cyclic of order p − 1.

Let Z be a random variable that is independent of the σ-algebra generated by B < sub > s </ sub >, s ≥ 0, and with finite second moment:

* Frobenius groups whose Fitting subgroup has arbitrarily large nilpotency class were constructed by Ito: Let q be a prime power, d a positive integer, and p a prime divisor of q − 1 with d ≤ p. Fix some field F of order q and some element z of this field of order p. The Frobenius complement H is the cyclic subgroup generated by the diagonal matrix whose i, ith entry is z < sup > i </ sup >.