On the Depth and Regularity of the Symmetric Algebra
نویسندگان
چکیده
Let (R,m) be a standard graded K-algebra whose defining ideal is componentwise linear. Using Gröbner basis techniques, bounds for the depth and the regularity of the symmetric algebra Sym(m) are given. MSC 2000: 13H10, 13P10, 13D02
منابع مشابه
Arens regularity and derivations of Hilbert modules with the certain product
Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$ is Arens regular. We also study the relationship between derivations of $A$ and $E$.
متن کاملArens Regularity and Weak Amenability of Certain Matrix Algebras
Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...
متن کاملStrong Topological Regularity and Weak Regularity of Banach Algebras
In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...
متن کاملArens regularity and cohomological properties of Banach lattice algebra
A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.
متن کاملNon-regularity of multiplications for general measure algebras
Let $fM(X)$ be the space of all finite regular Borel measures on $X$. A general measure algebra is a subspace of$fM(X)$,which is an $L$-space and has a multiplication preserving the probability measures. Let $cLsubseteqfM(X)$ be a general measure algebra on a locallycompact space $X$. In this paper, we investigate the relation between Arensregularity of $cL$ and the topology of $X$. We find...
متن کامل