[permalink] [id link]
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.
from
Wikipedia
Some Related Sentences
Let and P
Let P be the root of the unbalanced subtree, with R and L denoting the right and left children of P respectively.
Let denote the Bézier curve determined by the points P < sub > 0 </ sub >, P < sub > 1 </ sub >, ..., P < sub > n </ sub >.
Let P < sub > F </ sub > be the domain of a prefix-free universal computable function F. The constant Ω < sub > F </ sub > is then defined as
Let a light beam travel down the vertical line TP and bounce off from P. The beam's angle of inclination from the mirror is, so when it bounces off, its angle of inclination must be equal to.
# Let P ( x ) be a first-order formula in the language of Presburger arithmetic with a free variable x ( and possibly other free variables ).
Let P be the following property of partial functions F of one argument: P ( F ) means that F is defined for the argument ' 1 '.
Let us assume the bias is V and the barrier width is W. This probability, P, that an electron at z = 0 ( left edge of barrier ) can be found at z = W ( right edge of barrier ) is proportional to the wave function squared,
Let ρ, θ, and φ be spherical coordinates for the source point P. Here θ denotes the angle with the vertical axis, which is contrary to the usual American mathematical notation, but agrees with standard European and physical practice.
Let P < sup >− 1 </ sup > DP be an eigendecomposition of M, where P is a unitary complex matrix whose rows comprise an orthonormal basis of eigenvectors of M, and D is a real diagonal matrix whose main diagonal contains the corresponding eigenvalues.
Let be the columns of P, each multiplied by the ( real ) square root of the corresponding eigenvalue.
Let the total power radiated from a point source, for example, an omnidirectional isotropic antenna, be P. At large distances from the source ( compared to the size of the source ), this power is distributed over larger and larger spherical surfaces as the distance from the source increases.
Let K be R, C, or any field, and let V be the set P of all polynomials with coefficients taken from the field K.
Let further P < sub > Alice </ sub > denote the first plaintext block of Alice's message, let E denote encryption, and let P < sub > Eve </ sub > be Eve's guess for the first plaintext block.
Let and be
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 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 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 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 it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.
Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.
Let and finitely
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 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 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.
0.347 seconds.