منابع مشابه
On Ritt’s Polynomial Decomposition Theorems
Ritt studied the functional decomposition of a univariate complex polynomial f into prime (indecomposable) polynomials, f = u1 ◦ u2 ◦ · · · ◦ ur. His main achievement was a procedure for obtaining any decomposition of f from any other by repeatedly applying certain transformations. However, Ritt’s results provide no control on the number of times one must apply the basic transformations, which ...
متن کاملPrimary decomposition of the Mayr-Meyer ideals
Grete Hermann proved in H] that for any ideal I in an n-dimensional polynomial ring over the eld of rational numbers, if I is generated by polynomials f 1 ; : : : ; f k of degree at most d, then it is possible to write f = P r i f i such that each r i has degree at most deg f + (kd) (2 n). Mayr and Meyer in MM] found (generators) of ideals for which a doubly exponential bound in n is indeed ach...
متن کاملOn the Decomposition Theorems of Algebra
We shall in the following give an account of certain new ideas regarding the foundation of the so-called abstract algebra. These ideas, which have been developed only in the last couple of years, throw new light upon several of the basic problems of algebra. It should, however, be mentioned already at the beginning, that their application is in no way limited to algebra. They have originated pr...
متن کاملQuantum Stochastic Integrals and Doob-meyer Decomposition
Abstract. We show that for a quantum L-martingale (X(t)), p > 2, there exists a Doob-Meyer decomposition of the submartingale (|X(t)|). A noncommutative counterpart of a classical process continuous with probability one is introduced, and a quantum stochastic integral of such a process with respect to an L-martingale, p > 2, is constructed. Using this construction, the uniqueness of the Doob-Me...
متن کاملTowards a general Doob-Meyer decomposition theorem
Both the Doob-Meyer and the Graversen-Rao decomposition theorems can be proved following an approach based on predictable compensators of discretizations and weak-L technique, which was developed by K.M. Rao. It is shown that any decomposition obtained by Rao’s method gives predictability of compensators without additional assumptions (like submartingality in the original Doob-Meyer theorem or ...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1969
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10920