Indecomposability of polynomials via Jacobian matrix
نویسندگان
چکیده
منابع مشابه
Indecomposability of Polynomials via Jacobian Matrix
Indecomposable polynomials are a special class of absolutely irreducible polynomials. Some improvements of important effective results on absolute irreducibility have recently appeared using Ruppert’s matrix. In a similar way, we show in this paper that the use of a Jacobian matrix gives sharp bounds for the indecomposability problem.
متن کاملOn the indecomposability of polynomials
Applying a combinatorial lemma a new sufficient condition for the indecomposability of integer polynomials is established.
متن کاملIndecomposability of polynomials and related Diophantine equations
We present a new criterion for indecomposability of polynomials over Z. Using the criterion we obtain general finiteness result on polynomial Diophantine equation f(x) = g(y).
متن کاملIntegral and homothetic indecomposability with applications to irreducibility of polynomials
Being motivated by some methods for construction of homothetically indecomposable polytopes, we obtain new methods for construction of families of integrally indecomposable polytopes. As a result, we find new infinite families of absolutely irreducible multivariate polynomials over any field F . Moreover, we provide different proofs of some of the main results of Gao [2].
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 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: Journal of Algebra
سال: 2010
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2010.01.007