REGULARITY OF STRUCTURED RING SPECTRA AND
... in particular, the dual Steenrod algebra is a free module over it. By taking the identity of smash products HZ/2 ∧tmf HZ/2 ' (HZ/2 ∧ HZ/2) ∧HZ/2∧tmf HZ/2 and applying the Künneth spectral sequence of [EKMM97, IV 4.1], we find that ...
... in particular, the dual Steenrod algebra is a free module over it. By taking the identity of smash products HZ/2 ∧tmf HZ/2 ' (HZ/2 ∧ HZ/2) ∧HZ/2∧tmf HZ/2 and applying the Künneth spectral sequence of [EKMM97, IV 4.1], we find that ...
Relational semantics for full linear logic
... Algebraic semantics for substructural logics are given by partially ordered sets (posets) with additional operations on them (partially ordered algebras). Hence, the first step in obtaining relational semantics for substructural logics, using the method depicted in Figure 1, is to define canonical e ...
... Algebraic semantics for substructural logics are given by partially ordered sets (posets) with additional operations on them (partially ordered algebras). Hence, the first step in obtaining relational semantics for substructural logics, using the method depicted in Figure 1, is to define canonical e ...
THE JACOBSON DENSITY THEOREM AND APPLICATIONS We
... 1.1. Strictly Cyclic Modules and Modular Right Ideals. For a ring A with identity, cyclic modules are precisely those of the form a\A where a is a right ideal.1 What might be a useful analogous statement for a ring without identity? This question motivates what follows in this subsection. A module M ...
... 1.1. Strictly Cyclic Modules and Modular Right Ideals. For a ring A with identity, cyclic modules are precisely those of the form a\A where a is a right ideal.1 What might be a useful analogous statement for a ring without identity? This question motivates what follows in this subsection. A module M ...
ON NONASSOCIATIVE DIVISION ALGEBRAS^)
... such algebras can exist only when g has characteristic two, and then the elements of X which are not in g generate inseparable quadratic extensions of S- We shall also give a construction of such algebras. One of our main results is a generalization of the Wedderburn-Artin Theorem on finite division ...
... such algebras can exist only when g has characteristic two, and then the elements of X which are not in g generate inseparable quadratic extensions of S- We shall also give a construction of such algebras. One of our main results is a generalization of the Wedderburn-Artin Theorem on finite division ...
Proper holomorphic immersions into Stein manifolds with the density
... subset of Cd such that θ(C) ⊂ θ(B) are regular compact convex set in Cd . In the sequel, when speaking of convex subsets of V0 , we mean sets whose θ-images in Cd are convex. Replacing S by a Stein neighborhood of the compact strongly pseudoconvex domain D = A ∪ B, we may assume that D is O(S)-conve ...
... subset of Cd such that θ(C) ⊂ θ(B) are regular compact convex set in Cd . In the sequel, when speaking of convex subsets of V0 , we mean sets whose θ-images in Cd are convex. Replacing S by a Stein neighborhood of the compact strongly pseudoconvex domain D = A ∪ B, we may assume that D is O(S)-conve ...
MATH 103A Homework 5 - Solutions Due February 15, 2013
... Solution: G contains at least the elements e, x for x some non-identity element. We have proved that x G. Since x e, x e. By assumption that G contains no proper nontrivial subgroups, it must be the case that x G. We consider two cases. Case 1: x . By Theorem 4.1, for each i, ...
... Solution: G contains at least the elements e, x for x some non-identity element. We have proved that x G. Since x e, x e. By assumption that G contains no proper nontrivial subgroups, it must be the case that x G. We consider two cases. Case 1: x . By Theorem 4.1, for each i, ...
Parametric Integer Programming in Fixed Dimension
... fixed number of integer variables. Each S i is further equipped with a fixed number of mixed integer programs such that for each b ∈ S i the system Ax É b is integer feasible, if and only if one of the fixed number of “candidate solutions” obtained from plugging b in these associated mixed integer p ...
... fixed number of integer variables. Each S i is further equipped with a fixed number of mixed integer programs such that for each b ∈ S i the system Ax É b is integer feasible, if and only if one of the fixed number of “candidate solutions” obtained from plugging b in these associated mixed integer p ...
The Kazhdan-Lusztig polynomial of a matroid
... one does not recover the classical Kazhdan-Lusztig polynomials for the Coxeter group Sn from the braid matroid. Polo [Pol99] has shown that any polynomial with non-negative coefficients and constant term 1 appears as a Kazhdan-Lusztig polynomial associated to some symmetric group, while Kazhdan-Lus ...
... one does not recover the classical Kazhdan-Lusztig polynomials for the Coxeter group Sn from the braid matroid. Polo [Pol99] has shown that any polynomial with non-negative coefficients and constant term 1 appears as a Kazhdan-Lusztig polynomial associated to some symmetric group, while Kazhdan-Lus ...
A Ramsey space of infinite polyhedra and the random polyhedron
... the class KP. We also prove a universal property for ultrahomegeneous polyhedra and show that the automorphism group of the Fraı̈ssé limit of KP is extremely amenable, following [6]. A description of this Fraı̈ssé limit is given in Section 5; we call it the ordered random polyhedron. In Section 6, ...
... the class KP. We also prove a universal property for ultrahomegeneous polyhedra and show that the automorphism group of the Fraı̈ssé limit of KP is extremely amenable, following [6]. A description of this Fraı̈ssé limit is given in Section 5; we call it the ordered random polyhedron. In Section 6, ...
homogeneous locally compact groups with compact boundary
... subgroup M in G which is isomorphic to the positive reals under multiplication (Theorem II), and its closure in S is not compact. Therefore the arc component of 1 cannot be relatively compact. By homogeneity, there exists a homeomorphism of S mapping 1 onto e, and hence mapping the arc component of ...
... subgroup M in G which is isomorphic to the positive reals under multiplication (Theorem II), and its closure in S is not compact. Therefore the arc component of 1 cannot be relatively compact. By homogeneity, there exists a homeomorphism of S mapping 1 onto e, and hence mapping the arc component of ...
rings without a gorenstein analogue of the govorov–lazard theorem
... Abstract It was proved by Beligiannis and Krause that over certain Artin algebras, there are Gorenstein flat modules which are not direct limits of finitely generated Gorenstein projective modules. That is, these algebras have no Gorenstein analogue of the Govorov–Lazard theorem. We show that, in fa ...
... Abstract It was proved by Beligiannis and Krause that over certain Artin algebras, there are Gorenstein flat modules which are not direct limits of finitely generated Gorenstein projective modules. That is, these algebras have no Gorenstein analogue of the Govorov–Lazard theorem. We show that, in fa ...
Flatness
... Once we show this, the statement immediately follows from the previous theorem characterizing flatness via the first Tor. So, let F· → M be a free resolution of M . Then A/xA ⊗ F· is again an exact sequence, since the homology is TorA i (A/xA, M ), and these are all 0 since x is not a zero divisor. ...
... Once we show this, the statement immediately follows from the previous theorem characterizing flatness via the first Tor. So, let F· → M be a free resolution of M . Then A/xA ⊗ F· is again an exact sequence, since the homology is TorA i (A/xA, M ), and these are all 0 since x is not a zero divisor. ...
Nilpotence and Stable Homotopy Theory II
... from the sphere spectrum to a ring spectrum, is nilpotent if it is nilpotent when regarded as an element of the ring π∗ R. The main result of [7] is Theorem 2. In each of the above situations, the map f is nilpotent if the spectrum F is finite, and if M U∗ f = 0. In case the range of f is p-local, t ...
... from the sphere spectrum to a ring spectrum, is nilpotent if it is nilpotent when regarded as an element of the ring π∗ R. The main result of [7] is Theorem 2. In each of the above situations, the map f is nilpotent if the spectrum F is finite, and if M U∗ f = 0. In case the range of f is p-local, t ...