location:  Publications → journals
Search results

Search: All articles in the CMB digital archive with keyword extension

 Expand all        Collapse all Results 1 - 14 of 14

1. CMB Online first

Nasseh, Saeed
 On the Generalized Auslander-Reiten Conjecture under Certain Ring Extensions We show under some conditions that a Gorenstein ring $R$ satisfies the Generalized Auslander-Reiten Conjecture if and only if so does $R[x]$. When $R$ is a local ring we prove the same result for some localizations of $R[x]$. Keywords:Auslander-Reiten conjecture, finitistic extension degree, Gorenstein ringsCategories:13D07, 16E30, 16E65

2. CMB Online first

Nasseh, Saeed
 On the Generalized Auslander-Reiten Conjecture under Certain Ring Extensions We show under some conditions that a Gorenstein ring $R$ satisfies the Generalized Auslander-Reiten Conjecture if and only if so does $R[x]$. When $R$ is a local ring we prove the same result for some localizations of $R[x]$. Keywords:Auslander-Reiten conjecture, finitistic extension degree, Gorenstein ringsCategories:13D07, 16E30, 16E65

3. CMB 2013 (vol 57 pp. 254)

Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
 On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle The unitary extension principle (UEP) by Ron and Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the UEP-type wavelet systems that can be extended to a Parseval wavelet frame by adding just one UEP-type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators, and prove that this condition is also sufficient to ensure that an extension with just two generators is possible. Keywords:Bessel sequences, frames, extension of wavelet Bessel system to tight frame, wavelet systems, unitary extension principleCategories:42C15, 42C40

4. CMB 2012 (vol 56 pp. 870)

Wei, Changguo
 Note on Kasparov Product of $C^*$-algebra Extensions Using the Dadarlat isomorphism, we give a characterization for the Kasparov product of $C^*$-algebra extensions. A certain relation between $KK(A, \mathcal q(B))$ and $KK(A, \mathcal q(\mathcal k B))$ is also considered when $B$ is not stable and it is proved that $KK(A, \mathcal q(B))$ and $KK(A, \mathcal q(\mathcal k B))$ are not isomorphic in general. Keywords:extension, Kasparov product, $KK$-groupCategory:46L80

5. CMB 2011 (vol 56 pp. 116)

Krepski, Derek
 Central Extensions of Loop Groups and Obstruction to Pre-Quantization An explicit construction of a pre-quantum line bundle for the moduli space of flat $G$-bundles over a Riemann surface is given, where $G$ is any non-simply connected compact simple Lie group. This work helps to explain a curious coincidence previously observed between Toledano Laredo's work classifying central extensions of loop groups $LG$ and the author's previous work on the obstruction to pre-quantization of the moduli space of flat $G$-bundles. Keywords:loop group, central extension, prequantizationCategories:53D, 22E

6. CMB 2011 (vol 55 pp. 821)

Perez-Garcia, C.; Schikhof, W. H.
 New Examples of Non-Archimedean Banach Spaces and Applications The study carried out in this paper about some new examples of Banach spaces, consisting of certain valued fields extensions, is a typical non-archimedean feature. We determine whether these extensions are of countable type, have $t$-orthogonal bases, or are reflexive. As an application we construct, for a class of base fields, a norm $\|\cdot\|$ on $c_0$, equivalent to the canonical supremum norm, without non-zero vectors that are $\|\cdot\|$-orthogonal and such that there is a multiplication on $c_0$ making $(c_0,\|\cdot\|)$ into a valued field. Keywords:non-archimedean Banach spaces, valued field extensions, spaces of countable type, orthogonal basesCategories:46S10, 12J25

7. CMB 2007 (vol 50 pp. 588)

Labute, John; Lemire, Nicole; Mináč, Ján; Swallow, John
 Cohomological Dimension and Schreier's Formula in Galois Cohomology Let $p$ be a prime and $F$ a field containing a primitive $p$-th root of unity. Then for $n\in \N$, the cohomological dimension of the maximal pro-$p$-quotient $G$ of the absolute Galois group of $F$ is at most $n$ if and only if the corestriction maps $H^n(H,\Fp) \to H^n(G,\Fp)$ are surjective for all open subgroups $H$ of index $p$. Using this result, we generalize Schreier's formula for $\dim_{\Fp} H^1(H,\Fp)$ to $\dim_{\Fp} H^n(H,\Fp)$. Keywords:cohomological dimension, Schreier's formula, Galois theory, $p$-extensions, pro-$p$-groupsCategories:12G05, 12G10

8. CMB 2007 (vol 50 pp. 268)

Manuilov, V.; Thomsen, K.
 On the Lack of Inverses to $C^*$-Extensions Related to Property T Groups Using ideas of S. Wassermann on non-exact $C^*$-algebras and property T groups, we show that one of his examples of non-invertible $C^*$-extensions is not semi-invertible. To prove this, we show that a certain element vanishes in the asymptotic tensor product. We also show that a modification of the example gives a $C^*$-extension which is not even invertible up to homotopy. Keywords:$C^*$-algebra extension, property T group, asymptotic tensor $C^*$-norm, homotopyCategories:19K33, 46L06, 46L80, 20F99

9. CMB 2005 (vol 48 pp. 500)

Baracco, Luca
 Extension of Holomorphic Functions From One Side of a Hypersurface We give a new proof of former results by G. Zampieri and the author on extension of holomorphic functions from one side $\Omega$ of a real hypersurface $M$ of $\mathbb{C}^n$ in the presence of an analytic disc tangent to $M$, attached to $\bar\Omega$ but not to $M$. Our method enables us to weaken the regularity assumptions both for the hypersurface and the disc. Keywords:analytic discs, Poisson integral, holomorphic extensionCategories:32D10, 32V25

10. CMB 2004 (vol 47 pp. 191)

Grätzer, G.; Schmidt, E. T.
 Congruence Class Sizes in Finite Sectionally Complemented Lattices The congruences of a finite sectionally complemented lattice $L$ are not necessarily \emph{uniform} (any two congruence classes of a congruence are of the same size). To measure how far a congruence $\Theta$ of $L$ is from being uniform, we introduce $\Spec\Theta$, the \emph{spectrum} of $\Theta$, the family of cardinalities of the congruence classes of $\Theta$. A typical result of this paper characterizes the spectrum $S = (m_j \mid j < n)$ of a nontrivial congruence $\Theta$ with the following two properties: \begin{enumerate}[$(S_2)$] \item[$(S_1)$] $2 \leq n$ and $n \neq 3$. \item[$(S_2)$] $2 \leq m_j$ and $m_j \neq 3$, for all $j Keywords:congruence lattice, congruence-preserving extensionCategories:06B10, 06B15 11. CMB 2003 (vol 46 pp. 388) Lin, Huaxin  Tracially Quasidiagonal Extensions It is known that a unital simple$C^*$-algebra$A$with tracial topological rank zero has real rank zero. We show in this note that, in general, there are unital$C^*$-algebras with tracial topological rank zero that have real rank other than zero. Let$0\to J\to E\to A\to 0$be a short exact sequence of$C^*$-algebras. Suppose that$J$and$A$have tracial topological rank zero. It is known that$E$has tracial topological rank zero as a$C^*$-algebra if and only if$E$is tracially quasidiagonal as an extension. We present an example of a tracially quasidiagonal extension which is not quasidiagonal. Keywords:tracially quasidiagonal extensions, tracial rankCategories:46L05, 46L80 12. CMB 2001 (vol 44 pp. 266) Cencelj, M.; Dranishnikov, A. N.  Extension of Maps to Nilpotent Spaces We show that every compactum has cohomological dimension$1$with respect to a finitely generated nilpotent group$G$whenever it has cohomological dimension$1$with respect to the abelianization of$G$. This is applied to the extension theory to obtain a cohomological dimension theory condition for a finite-dimensional compactum$X$for extendability of every map from a closed subset of$X$into a nilpotent$\CW$-complex$M$with finitely generated homotopy groups over all of$X$. Keywords:cohomological dimension, extension of maps, nilpotent group, nilpotent spaceCategories:55M10, 55S36, 54C20, 54F45 13. CMB 2000 (vol 43 pp. 208) Matoušková, Eva  Extensions of Continuous and Lipschitz Functions We show a result slightly more general than the following. Let$K$be a compact Hausdorff space,$F$a closed subset of$K$, and$d$a lower semi-continuous metric on$K$. Then each continuous function$f$on$F$which is Lipschitz in$d$admits a continuous extension on$K$which is Lipschitz in$d$. The extension has the same supremum norm and the same Lipschitz constant. As a corollary we get that a Banach space$X$is reflexive if and only if each bounded, weakly continuous and norm Lipschitz function defined on a weakly closed subset of$X$admits a weakly continuous, norm Lipschitz extension defined on the entire space$X$. Keywords:extension, continous, Lipschitz, Banach spaceCategories:54C20, 46B10 14. CMB 1999 (vol 42 pp. 335) Kim, Goansu; Tang, C. Y.  Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups We derive a necessary and sufficient condition for HNN-extensions of cyclic subgroup separable groups with cyclic associated subgroups to be cyclic subgroup separable. Applying this, we explicitly characterize the residual finiteness and the cyclic subgroup separability of HNN-extensions of abelian groups with cyclic associated subgroups. We also consider these residual properties of HNN-extensions of nilpotent groups with cyclic associated subgroups. Keywords:HNN-extension, nilpotent groups, cyclic subgroup separable$(\pi_c)\$, residually finiteCategories:20E26, 20E06, 20F10