ON QUILLEN`S THEOREM A FOR POSETS 1. Introduction In his
... with a third complex are also homotopy equivalent. In particular, the join of a contractible complex with another complex is contractible. For simplicity we will identify a simplicial complex with its geometric realization. The following result [26, 1.3] is a particular case of the well known fact t ...
... with a third complex are also homotopy equivalent. In particular, the join of a contractible complex with another complex is contractible. For simplicity we will identify a simplicial complex with its geometric realization. The following result [26, 1.3] is a particular case of the well known fact t ...
Finite group schemes
... Let G/k be a group scheme over some field k. Let G0 denote the connected component of G that contains e. One expects that G0 is a subgroup scheme of G. This is indeed true. One needs to prove that the image of G0 ×k G0 ⊂ G ×k G under the multiplication map m : G ×k G → G is contained in G0 . We are ...
... Let G/k be a group scheme over some field k. Let G0 denote the connected component of G that contains e. One expects that G0 is a subgroup scheme of G. This is indeed true. One needs to prove that the image of G0 ×k G0 ⊂ G ×k G under the multiplication map m : G ×k G → G is contained in G0 . We are ...
![A Note on Locally Nilpotent Derivations and Variables of k[X,Y,Z]](http://s1.studyres.com/store/data/005260578_1-37b1c4bbe55693dae2b5b98fbc2c091d-300x300.png)
A Note on Locally Nilpotent Derivations and Variables of k[X,Y,Z]
... field C of complex numbers and which involves a finite number of points and of varieties, remains valid over any universal domain (i.e., over an algebraically closed field with infinite transcendence degree over the prime field) of characteristic zero. In this form the principle was proved by Eklof ...
... field C of complex numbers and which involves a finite number of points and of varieties, remains valid over any universal domain (i.e., over an algebraically closed field with infinite transcendence degree over the prime field) of characteristic zero. In this form the principle was proved by Eklof ...
1 Valuations of the field of rational numbers
... Q[x]/(P ) is a field, finite extension of Q. All finite extensions of Q are of this form since it is known that all finite extensions of a field in characteristic zero can be generated by a single element [?, V,4.6]. Let L be a finite extension of degree n of Q. For every element α ∈ L, the multipl ...
... Q[x]/(P ) is a field, finite extension of Q. All finite extensions of Q are of this form since it is known that all finite extensions of a field in characteristic zero can be generated by a single element [?, V,4.6]. Let L be a finite extension of degree n of Q. For every element α ∈ L, the multipl ...
CH2
... A dual of a boolean expression is formed by replacing: AND’s OR’s, OR’s AND’s, 1’s 0’s, and 0’s 1’s. Variables and their complements are left alone. If two boolean expressions are equal, then their duals are equal! Example: (X+Y’)Y = XY XY’ + Y = X + Y ...
... A dual of a boolean expression is formed by replacing: AND’s OR’s, OR’s AND’s, 1’s 0’s, and 0’s 1’s. Variables and their complements are left alone. If two boolean expressions are equal, then their duals are equal! Example: (X+Y’)Y = XY XY’ + Y = X + Y ...
von Neumann Algebras - International Mathematical Union
... factor. In the last of their papers, Murray and von Neumann had shown that, though there exists more than one factor of type 1^ (they exhibited 2, in 1968 D, MacDuff constructed a continuum of them) there is among them, only one having the following approximation property: V finite subset F of N, Ve ...
... factor. In the last of their papers, Murray and von Neumann had shown that, though there exists more than one factor of type 1^ (they exhibited 2, in 1968 D, MacDuff constructed a continuum of them) there is among them, only one having the following approximation property: V finite subset F of N, Ve ...
Algorithms in algebraic number theory
... turn out to have the widest application range, exactly because it was not done with any specific application in mind. There is a small price to be paid for admission to this paradise. Algorithms and their running times can only be investigated mathematically if they are given exact definitions, and ...
... turn out to have the widest application range, exactly because it was not done with any specific application in mind. There is a small price to be paid for admission to this paradise. Algorithms and their running times can only be investigated mathematically if they are given exact definitions, and ...
