منابع مشابه
Hilbert Polynomials of Non-standard Bigraded Algebras
If R is standard bigraded, i.e. R is generated by elements of bidegrees (1, 0) and (0, 1), then HR(u, v) is equal to a polynomial in u, v for u, v large enough [Ba], [KMV], [W]. This fact does not hold if R is not standard bigraded. In this paper we will study the case R is generated by elements of bidegrees (1, 0), (d1, 1), . . . , (dr, 1), where d1, . . . , dr are non-negative integers. This ...
متن کاملCentral polynomials for matrix algebras over the Grassmann algebra
In this work, we describe a method to construct central polynomials for F -algebras where F is a field of characteristic zero. The main application deals with the T -prime algebras Mn(E), where E is the infinitedimensional Grassmann algebra over F , which play a fundamental role in the theory of PI-algebras. The method is based on the explicit decomposition of the group algebra FSn. AMS Classif...
متن کاملNILPOTENT GRAPHS OF MATRIX ALGEBRAS
Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...
متن کاملHigher numerical ranges of matrix polynomials
Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...
متن کاملGeneralized numerical ranges of matrix polynomials
In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.2307/1996962