Expand all Collapse all | Results 51 - 75 of 76 |
51. CMB 2002 (vol 45 pp. 451)
Coordinatization Theorems For Graded Algebras In this paper we study simple associative algebras with finite
$\mathbb{Z}$-gradings. This is done using a simple algebra $F_g$
that has been constructed in Morita theory from a bilinear form
$g\colon U\times V\to A$ over a simple algebra $A$. We show that
finite $\mathbb{Z}$-gradings on $F_g$ are in one to one
correspondence with certain decompositions of the pair $(U,V)$. We
also show that any simple algebra $R$ with finite
$\mathbb{Z}$-grading is graded isomorphic to $F_g$ for some
bilinear from $g\colon U\times V \to A$, where the grading on $F_g$
is determined by a decomposition of $(U,V)$ and the coordinate
algebra $A$ is chosen as a simple ideal of the zero component $R_0$
of $R$. In order to prove these results we first prove similar
results for simple algebras with Peirce gradings.
Category:16W50 |
52. CMB 2002 (vol 45 pp. 388)
AlgÃ¨bres simples centrales de degrÃ© 5 et $E_8$ As a consequence of a theorem of Rost-Springer, we establish that the
cyclicity problem for central simple algebra of degree~5 on fields
containg a fifth root of unity is equivalent to the study of
anisotropic elements of order 5 in the split group of type~$E_8$.
Keywords:algÃ¨bres simples centrales, cohomologie galoisienne Categories:16S35, 12G05, 20G15 |
53. CMB 2002 (vol 45 pp. 448)
Erratum: A Characterization of Left Perfect Rings An error in {\it A characterization of left perfect rings},
Canad. Math. Bull. (3) {\bf 38}(1995), 382--384, is indicated
and the consequences identified.
Category:16L30 |
54. CMB 2002 (vol 45 pp. 11)
Polycharacters of Cocommutative Hopf Algebras In this paper we extend a well-known theorem of M.~Scheunert on
skew-symmetric bicharacters of groups to the case of skew-symmetric
bicharacters on arbitrary cocommutative Hopf algebras over a field of
characteristic not 2. We also classify polycharacters on (restricted)
enveloping algebras and bicharacters on divided power algebras.
Categories:16W30, 16W55 |
55. CMB 2001 (vol 44 pp. 27)
Normal Subloops in the Integral Loop Ring of an $\RA$ Loop We show that an $\RA$ loop has a torsion-free normal complement in the
loop of normalized units of its integral loop ring. We also
investigate whether an $\RA$ loop can be normal in its unit loop.
Over fields, this can never happen.
Categories:20N05, 17D05, 16S34, 16U60 |
56. CMB 2000 (vol 43 pp. 413)
Non-Isomorphic Maximal Orders with Isomorphic Matrix Rings We construct a countably infinite family of pairwise non-isomorphic
maximal ${\mathbb Q}[X]$-orders such that the full $2$ by $2$
matrix rings over these orders are all isomorphic.
Categories:16S50, 16H05, 16N60 |
57. CMB 2000 (vol 43 pp. 60)
Trivial Units in Group Rings Let $G$ be an arbitrary group and let $U$ be a subgroup of the
normalized units in $\mathbb{Z}G$. We show that if $U$ contains $G$
as a subgroup of finite index, then $U = G$. This result can be used
to give an alternative proof of a recent result of Marciniak and
Sehgal on units in the integral group ring of a crystallographic group.
Keywords:units, trace, finite conjugate subgroup Categories:16S34, 16U60 |
58. CMB 2000 (vol 43 pp. 100)
A Gorenstein Ring with Larger Dilworth Number than Sperner Number A counterexample is given to a conjecture of Ikeda by finding a class of
Gorenstein rings of embedding dimension $3$ with larger Dilworth number than
Sperner number. The Dilworth number of $A[Z/pZ\oplus Z/pZ]$ is computed
when $A$ is an unramified principal Artin local ring.
Categories:13E15, 16S34 |
59. CMB 2000 (vol 43 pp. 79)
Cyclotomic Schur Algebras and Blocks of Cyclic Defect An explicit classification is given of blocks of cyclic defect of
cyclotomic Schur algebras and of cyclotomic Hecke algebras, over
discrete valuation rings.
Categories:20G05, 20C20, 16G30, 17B37, 57M25 |
60. CMB 2000 (vol 43 pp. 3)
Resolutions of Associative and Lie Algebras Certain canonical resolutions are described for free associative and
free Lie algebras in the category of non-associative algebras. These
resolutions derive in both cases from geometric objects, which in turn
reflect the combinatorics of suitable collections of leaf-labeled
trees.
Keywords:resolutions, homology, Lie algebras, associative algebras, non-associative algebras, Jacobi identity, leaf-labeled trees, associahedron Categories:18G10, 05C05, 16S10, 17B01, 17A50, 18G50 |
61. CMB 1999 (vol 42 pp. 298)
Semigroup Algebras and Maximal Orders We describe contracted semigroup algebras of Malcev nilpotent
semigroups that are prime Noetherian maximal orders.
Categories:16S36, 16H05, 20M25 |
62. CMB 1999 (vol 42 pp. 401)
Lie Derivations in Prime Rings With Involution Let $R$ be a non-GPI prime ring with involution and characteristic
$\neq 2,3$. Let $K$ denote the skew elements of $R$, and $C$ denote
the extended centroid of $R$. Let $\delta$ be a Lie derivation of $K$
into itself. Then $\delta=\rho+\epsilon$ where $\epsilon$ is an
additive map into the skew elements of the extended centroid of $R$
which is zero on $[K,K]$, and $\rho$ can be extended to an ordinary
derivation of $\langle K\rangle$ into $RC$, the central closure.
Categories:16W10, 16N60, 16W25 |
63. CMB 1999 (vol 42 pp. 371)
Prime and Primary Ideals in a PrÃ¼fer Order in a Simple Artinian Ring with Finite Dimension over its Center |
Prime and Primary Ideals in a PrÃ¼fer Order in a Simple Artinian Ring with Finite Dimension over its Center Let $Q$ be a simple Artinian ring with finite dimension over its center.
An order $R$ in $Q$ is said to be {\it Pr\"ufer\/} if any one-sided
$R$-ideal is a progenerator. We study prime and primary ideals of a
Pr\"ufer order under the condition that the center is Pr\"ufer.
Also we characterize branched and unbranched prime ideals of a
Pr\"ufer order.
Categories:16H05, 16L30 |
64. CMB 1999 (vol 42 pp. 174)
Rings With Comparability The class of rings studied in this paper properly contains the
class of right distributive rings which have at least one
completely prime ideal in the Jacobson radical. Amongst other
results we study prime and semiprime ideals, right noetherian rings
with comparability and prove a structure theorem for rings with
comparability. Several examples are also given.
Categories:16U99, 16P40, 16D14, 16N60 |
65. CMB 1998 (vol 41 pp. 481)
The periodic radical of group rings and incidence algebras Let $R$ be a ring with $1$ and $P(R)$ the periodic radical of $R$.
We obtain necessary and sufficient conditions for $P(\RG) = 0$ when
$\RG$ is the group ring of an $\FC$ group $G$ and $R$ is commutative. We
also obtain a complete description of $P\bigl(I (X, R)\bigr)$ when
$I(X,R)$ is the incidence algebra of a locally finite partially
ordered set $X$ and $R$ is commutative.
Categories:16S34, 16S99, 16N99 |
66. CMB 1998 (vol 41 pp. 452)
Dependent automorphisms in prime rings For each $n\geq 4$ we construct a class of examples of a minimal
$C$-dependent set of $n$ automorphisms of a prime ring $R$, where $C$
is the extended centroid of $R$. For $n=4$ and $n=5$ it is shown that
the preceding examples are completely general, whereas for $n=6$ an
example is given which fails to enjoy any of the nice properties of
the above example.
Categories:16N60, 16W20 |
67. CMB 1998 (vol 41 pp. 359)
Embedding the Hopf automorphism group into the Brauer group Let $H$ be a faithfully projective Hopf algebra over a commutative
ring $k$. In \cite{CVZ1, CVZ2} we defined the Brauer group
$\BQ(k,H)$ of $H$ and an homomorphism $\pi$ from Hopf automorphism
group $\Aut_{\Hopf}(H)$ to $\BQ(k,H)$. In this paper, we show that
the morphism $\pi$ can be embedded into an exact sequence.
Categories:16W30, 13A20 |
68. CMB 1998 (vol 41 pp. 261)
A simple ring over which proper cyclics are continuous is a $\PCI$-ring It is shown that simple rings over which proper cyclic right modules are
continuous coincide with simple right $\PCI$-rings, introduced by Faith.
Keywords:Simple rings, $\PCI$-rings, $\PCQI$-rings, continuous modules,, quasi-continuous modules Categories:16D50, 16D70 |
69. CMB 1998 (vol 41 pp. 81)
The cardinality of the center of a $\PI$ ring The main result shows that if $R$ is a semiprime ring satisfying
a polynomial identity, and if $Z(R)$ is the center of $R$, then
$\card R \leq 2^{\card Z(R)}$. Examples show that this bound can
be achieved, and that the inequality fails to hold for rings which
are not semiprime.
Categories:16R20, 16N60, 16R99, 16U50 |
70. CMB 1998 (vol 41 pp. 118)
On permanental identities of symmetric and skew-symmetric matrices in characteristic \lowercase{$p$} |
On permanental identities of symmetric and skew-symmetric matrices in characteristic \lowercase{$p$} Let $M_n(F)$ be the algebra of $n \times n$
matrices over a field $F$ of characteristic $p>2$ and let $\ast$ be an
involution on $M_n(F)$. If $s_1, \ldots, s_r$ are symmetric
variables we determine the smallest $r$ such that the polynomial
$$
P_{r}(s_1, \ldots, s_{r}) = \sum_{\sigma \in {\cal
S}_r}s_{\sigma(1)}\cdots s_{\sigma(r)}
$$
is a $\ast$-polynomial identity of $M_n(F)$ under either the
symplectic or the transpose involution. We also prove an analogous
result for the polynomial
$$
C_r(k_1, \ldots, k_r, k'_1, \ldots, k'_r) = \sum_
{\sigma, \tau \in {\cal S}_r}k_{\sigma(1)}k'_{\tau(1)}\cdots
k_{\sigma(r)}k'_{\tau(r)}
$$
where $k_1, \ldots, k_r, k'_1, \ldots, k'_r$ are skew
variables under the transpose involution.
Category:16R50 |
71. CMB 1998 (vol 41 pp. 109)
On generalized third dimension subgroups Let $G$ be any group, and $H$ be a normal subgroup of $G$. Then M.~Hartl
identified the subgroup $G \cap(1+\triangle^3(G)+\triangle(G)\triangle(H))$
of $G$. In this note we give an independent proof of the result of Hartl,
and we identify two subgroups
$G\cap(1+\triangle(H)\triangle(G)\triangle(H)+\triangle([H,G])\triangle(H))$,
$G\cap(1+\triangle^2(G)\triangle(H)+\triangle(K)\triangle(H))$ of $G$ for
some subgroup $K$ of $G$ containing $[H,G]$.
Categories:20C07, 16S34 |
72. CMB 1998 (vol 41 pp. 79)
An answer to a question of Kegel on sums of rings We construct a ring $R$ which is a sum of two subrings
$A$ and $B$ such that the Levitzki radical of $R$ does not
contain any of the hyperannihilators of $A$ and $B$. This
answers an open question asked by Kegel in 1964.
Categories:16N40, 16N60 |
73. CMB 1997 (vol 40 pp. 221)
On semiregular rings whose finitely generated modules embed in free modules We consider rings as in the title and find the precise obstacle for them not
to be Quasi-Frobenius, thus shedding new light on an old open question in
Ring Theory. We also find several partial affirmative answers for that
question.
Categories:16D10, 16L60, 16N20 |
74. CMB 1997 (vol 40 pp. 198)
The ${\cal J}_0$-radical of a matrix nearring can be intermediate An example is constructed to show that the ${\cal J}_0$-radical of a matrix
nearring can be an intermediate ideal. This solves a conjecture put forward
in [1].
Categories:16Y30, 16S50, 16D25 |
75. CMB 1997 (vol 40 pp. 103)
The transfer of a commutator law from a nil-ring to its adjoint group For every field $F$ of characteristic $p\geq 0$,
we construct an example of a finite dimensional nilpotent
$F$-algebra $R$ whose adjoint group $A(R)$ is not
centre-by-metabelian, in spite of the fact that $R$ is Lie
centre-by-metabelian
and satisfies the identities $x^{2p}=0$ when $p>2$ and
$x^8=0$ when $p=2$. The
existence of such algebras answers a question raised by
A.~E.~Zalesskii, and is in contrast to
positive results obtained by Krasilnikov, Sharma and Srivastava
for Lie metabelian rings
and by Smirnov for the class Lie centre-by-metabelian nil-algebras
of exponent 4 over a field of characteristic 2 of cardinality at least 4.
Categories:16U60, 17B60 |