0000000001333867
AUTHOR
La Mattina, Daniela
showing 4 related works from this author
Some results on ∗-minimal algebras with involution
2009
Let $(A, *)$ be an associative algebra with involution over a field $F$ of characteristic zero, $T_*(A)$ the ideal of $*$-polynomial identities of $A$ and $c_n(A, *),$ $n=1, 2, \ldots$, the corresponding sequence of $*$-codimensions. Recall that $c_n(A, *)$ is the dimension of the space of multilinear polynomials in $n$ variables in the corresponding relatively free algebra with involution of countable rank. \par When $A$ is a finite dimensional algebra, Giambruno and Zaicev [J. Algebra 222 (1999), no. 2, 471–484; MR1734235 (2000i:16046)] proved that the limit $$\exp(A, *)=\lim_{n\to \infty}\sqrt[n]{c_n(A, *)}$$ exists and is an integer called the $*$-exponent of $A.$ \par Among finite dime…
Supervarieties and *-varieties of algebras of polynomial growth
2008
We study the sequence of supercodimensions and *-codimensions of unitary algebras.
The central polynomials of the infinite-dimensional unitary and nonunitary Grassmann algebras
2010
For a fixed field $k$, let $k_0\langle X\rangle$ and $k_1\langle X \rangle$ denote respectively the free nonunitary associative $k$-algebra and the free unitary associative $k$-algebra on the countable set $X=\{x_1, x_2, \ldots\}.$ A polynomial $f\in k_i\langle X\rangle$ is called a central polynomial for an associative algebra $A$ if every evaluation of $f$ on $A$ lies in the center of $A.$ The set of all central polynomials of $A$ is a $T$-space of $k_i\langle X\rangle,$ i.e, a subspace closed under all endomorphisms of $k_i\langle X\rangle.$ In this paper the authors describe the T-space of central polynomials for both the unitary and the nonunitary infinite-dimensional Grassmann algebra…
Graded central polynomials for the matrix algebra of order two
2009
Let K be an infinite integral domain and $A=M_2(K)$ the algebra of $2\times 2$ matrices over $K$. The authors consider the natural $\mathbb{Z}_2$-grading of $A$ obtained by requiring that the diagonal matrices and the off-diagonal matrices are of homogeneous degree $0$ and $1$, respectively. When $K$ is a field, a basis of the graded identities of $A$ was described in [O. M. Di Vincenzo, On the graded identities of $M_{1,1}(E).$ Israel J. Math. 80 (1992), no. 3, 323-–335] in case $\mbox{char}\, K = 0$ and in [P. E. Koshlukov and S. S. de Azevedo, Graded identities for T-prime algebras over fields of positive characteristic. Israel J. Math. 128 (2002), 157-–176] when $K$ is infinite and $\mb…