Search results for " Ring"
showing 10 items of 478 documents
A-Codes from Rational Functions over Galois Rings
2006
In this paper, we describe authentication codes via (generalized) Gray images of suitable codes over Galois rings. Exponential sums over these rings help determine--or bound--the parameters of such codes.
Interpolation and approximation in L2(γ)
2007
Assume a standard Brownian motion W=(W"t)"t"@?"["0","1"], a Borel function f:R->R such that f(W"1)@?L"2, and the standard Gaussian measure @c on the real line. We characterize that f belongs to the Besov space B"2","q^@q(@c)@?(L"2(@c),D"1","2(@c))"@q","q, obtained via the real interpolation method, by the behavior of a"X(f(X"1);@t)@[email protected]?f(W"1)-P"X^@tf(W"1)@?"L"""2, where @t=(t"i)"i"="0^n is a deterministic time net and P"X^@t:L"2->L"2 the orthogonal projection onto a subspace of 'discrete' stochastic integrals x"[email protected]?"i"="1^nv"i"-"1(X"t"""i-X"t"""i"""-"""1) with X being the Brownian motion or the geometric Brownian motion. By using Hermite polynomial expansions the…
Bounded elements of C*-inductive locally convex spaces
2013
The notion of bounded element of C*-inductive locally convex spaces (or C*-inductive partial *-algebras) is introduced and discussed in two ways: The first one takes into account the inductive structure provided by certain families of C*-algebras; the second one is linked to the natural order of these spaces. A particular attention is devoted to the relevant instance provided by the space of continuous linear maps acting in a rigged Hilbert space.
Identities of PI-Algebras Graded by a Finite Abelian Group
2011
We consider associative PI-algebras over an algebraically closed field of zero characteristic graded by a finite abelian group G. It is proved that in this case the ideal of graded identities of a G-graded finitely generated PI-algebra coincides with the ideal of graded identities of some finite dimensional G-graded algebra. This implies that the ideal of G-graded identities of any (not necessary finitely generated) G-graded PI-algebra coincides with the ideal of G-graded identities of the Grassmann envelope of a finite dimensional (G × ℤ2)-graded algebra, and is finitely generated as GT-ideal. Similar results take place for ideals of identities with automorphisms.
Lie nilpotence of group rings
1993
Let FG be the group algebra of a group G over a field F. Denote by ∗ the natural involution, (∑fi gi -1. Let S and K denote the set of symmetric and skew symmetric and skew symmetric elements respectively with respect to this involutin. It is proved that if the characteristic of F is zero p≠2 and G has no 2-elements, then the Lie nilpotence of S or K implies the Lie nilpotence of FG.
Derivations on a Lie Ideal
1988
AbstractIn this paper we prove the following result: let R be a prime ring with no non-zero nil left ideals whose characteristic is different from 2 and let U be a non central Lie ideal of R.If d ≠ 0 is a derivation of R such that d(u) is invertible or nilpotent for all u ∈ U, then either R is a division ring or R is the 2 X 2 matrices over a division ring. Moreover in the last case if the division ring is non commutative, then d is an inner derivation of R.
Multialternating graded polynomials and growth of polynomial identities
2012
Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codimensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. In particular we show it is an integer. The result was proviously known in case G is abelian.
The Herzog-Vasconcelos conjecture for affine semigroup rings
1999
Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.
Associative rings with metabelian adjoint group
2004
Abstract The set of all elements of an associative ring R, not necessarily with a unit element, forms a monoid under the circle operation r∘s=r+s+rs on R whose group of all invertible elements is called the adjoint group of R and denoted by R°. The ring R is radical if R=R°. It is proved that a radical ring R is Lie metabelian if and only if its adjoint group R° is metabelian. This yields a positive answer to a question raised by S. Jennings and repeated later by A. Krasil'nikov. Furthermore, for a ring R with unity whose multiplicative group R ∗ is metabelian, it is shown that R is Lie metabelian, provided that R is generated by R ∗ and R modulo its Jacobson radical is commutative and arti…
Radical Rings with Engel Conditions
2000
Abstract An associative ring R without unity is called radical if it coincides with its Jacobson radical, which means that the set of all elements of R forms a group denoted by R ∘ under the circle operation r ∘ s = r + s + rs on R . It is proved that, for a radical ring R , the group R ∘ satisfies an n -Engel condition for some positive integer n if and only if R is m -Engel as a Lie ring for some positive integer m depending only on n .