共查询到20条相似文献,搜索用时 15 毫秒
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Leo G. Chouinard II 《代数通讯》2013,41(16):1519-1537
A category-theoretic definition of transfer is given, and its basic properties are explored. As applications, a special case due to Mitchell is used to establish a result about integral extensions of arithmetical rings, and non-classical transfers between modules over group rings are used to obtain information about localizations of group rings by central elements which are not in the coefficient ring 相似文献
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Let σ be an endomorphism of the free group on two generators and Φσ the trace map associated with σ. A polynomial P is said to be periodic for σ if, for some positive integer n, it is invariant under , i.e., . In this note we study the structure of the ring of periodic polynomials for σ. 相似文献
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Eli Aljadeff 《Israel Journal of Mathematics》1994,86(1-3):221-232
LetK be a commutative ring with a unit element 1. Let Γ be a finite group acting onK via a mapt: Γ→Aut(K). For every subgroupH≤Γ define tr
H
:K→K
H
by tr
h
(x)=Σσ∈H
σ(x). We proveTheorem: trΓ
is surjective onto
K
Γ
if and only if tr
P
is surjective onto K
P
for every (cyclic) prime order subgroup P of Γ.
This is false for certain non-commutative ringsK. 相似文献
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Davide L. Ferrario 《Journal of Fixed Point Theory and Applications》2011,10(1):113-127
A Reidemeister trace for fibred maps is defined as the alternating sum of suitable (elementary) traces for linear morphisms of fibred cellular free modules with local coefficients. This invariant extends in a natural way the classical construction of the generalized Lefschetz number??Reidemeister trace??to the category of fibred CW-complexes. 相似文献
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R.A Mollin 《Journal of Number Theory》1983,17(2):165-175
For a given positive integer m and an algebraic number field K necessary and sufficient conditions for the mth cyclotomic polynomial to have K-integral solutions modulo a given integer of K are given. Among applications thereof are: that the solvability of the cyclotomic polynomial mod an integer yields information about the class number of related number fields; and about representation of integers by binary quadratic forms. The latter extends previous work of the author. Moreover some information is obtained pertaining to when an integer of K is the norm of an integer in a given quadratic extension of K. Finally an explicit determination of the pqth cyclotomic polynomial for distinct primes p and q is provided, and known results in the literature as well as generalizations thereof are obtained. 相似文献
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Transfer maps are closely related to the problem of splitting a homotopy equivalence along a submanifold and with the problem of surgery on a pair of manifolds. In the present paper, we describe relations between various transfer maps for a triple of embedded manifolds. 相似文献
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Shabnam Akhtari 《Journal of Number Theory》2008,128(4):884-894
In this article, we study the cyclotomic polynomials of degree N−1 with coefficients restricted to the set {+1,−1}. By a cyclotomic polynomial we mean any monic polynomial with integer coefficients and all roots of modulus 1. By a careful analysis of the effect of Graeffe's root squaring algorithm on cyclotomic polynomials, P. Borwein and K.K. Choi gave a complete characterization of all cyclotomic polynomials with odd coefficients. They also proved that a polynomial p(x) with coefficients ±1 of even degree N−1 is cyclotomic if and only if p(x)=±Φp1(±x)Φp2(±xp1)?Φpr(±xp1p2?pr−1), where N=p1p2?pr and the pi are primes, not necessarily distinct. Here is the pth cyclotomic polynomial. Based on substantial computation, they also conjectured that this characterization also holds for polynomials of odd degree with ±1 coefficients. We consider the conjecture for odd degree here. Using Ramanujan's sums, we solve the problem for some special cases. We prove that the conjecture is true for polynomials of degree α2pβ−1 with odd prime p or separable polynomials of any odd degree. 相似文献
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Pieter Moree 《Journal of Number Theory》2009,129(3):667-680
Let Ψn(x) be the monic polynomial having precisely all non-primitive nth roots of unity as its simple zeros. One has Ψn(x)=(xn−1)/Φn(x), with Φn(x) the nth cyclotomic polynomial. The coefficients of Ψn(x) are integers that like the coefficients of Φn(x) tend to be surprisingly small in absolute value, e.g. for n<561 all coefficients of Ψn(x) are ?1 in absolute value. We establish various properties of the coefficients of Ψn(x), especially focusing on the easiest non-trivial case where n is composed of 3 distinct odd primes. 相似文献
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David P. Roberts 《Proceedings of the American Mathematical Society》2007,135(7):1959-1967
For each prime power , we realize the classical cyclotomic polynomial as one of a collection of different polynomials in . We show that the new polynomials are similar to in many ways, including that their discriminants all have the form . We show also that the new polynomials are more complicated than in other ways, including that their complex roots are generally fractal in appearance.
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Benjamin Enriquez 《Selecta Mathematica, New Series》2007,13(3):391-463
We develop a cyclotomic analogue of the theory of associators. Using a trigonometric version of the universal KZ equations,
we prove the formality of a morphism , where B
n
1 is a braid group of type B. The formality isomorphism depends algebraically on a series ΨKZ, the “KZ pseudotwist”. We study the scheme of pseudotwists and show that it is a torsor under a group GTM(N, k), mapping to Drinfeld’s group GT(k), and whose Lie algebra is isomorphic to its associated graded (N, k). We prove that Ihara’s subgroup GTK of the Grothendieck–Teichmüller group, defined using distribution relations, in fact
coincides with it. We show that the subscheme of pseudotwists satisfying distribution relations is a subtorsor. We study the
corresponding analogue (N, k) of (N, k); it is a graded Lie algebra with an action of , and we give a lower bound for the character of its space of generators.
相似文献
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Domenico Mucci 《manuscripta mathematica》2009,128(4):421-441
We deal with strong density results of smooth maps between two manifolds and in the fractional spaces given by the traces of Sobolev maps in W
1,p
. 相似文献
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A radical extension of the rational numbers is a field generated by an element having a power in , and a cyclotomic extension is an extension generated by a root of unity. We show that a radical extension that is almost Galois over is almost cyclotomic. More precisely, we prove that if is radical with Galois closure , then contains a cyclotomic field such that the degree is bounded above by an almost linear function of . In particular, if is Galois, it contains a cyclotomic field such that .