We theoretically study the Kondo effect in a quantum dot embedded in an Aharonov-Bohm ring, using the "poor man's" scaling method. Analytical expressions of the Kondo temperature TK are given as a function of magnetic flux Φ penetrating the ring. In this Kondo problem, there are two characteristic lengths, Lc=ℏvF∕|ε̃0| and LK = ħvF = TK, where vF is the Fermi velocity and ε̃0 is the renormalized ...

In this paper, we establish two results concerning algebraic (C,+)-actions on C. First of all, let φ be an algebraic (C,+)-action on C3. By a result of Miyanishi, its ring of invariants is isomorphic to C[t1, t2]. If f1, f2 generate this ring, the quotient map of φ is the map F : C3 → C2, x 7→ (f1(x), f2(x)). By using some topological arguments, we prove that F is always surjective. Secondly we...

We prove new height inequalities for determinantal ideals in a regular local ring, or more generally in a local ring of given embedding codimension. Our theorems extend and sharpen results of Faltings and Bruns. Introduction. Let φ be a map of vector bundles on a variety X. A wellknown theorem of Eagon and Northcott [EN] gives an upper bound for the codimension of the locus where φ has rank ≤ s...

Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.

Using Gröbner Basis, we introduce a general algorithm to determine the additive structure of a module, when we know about it using indirect information about its structure. We apply the algorithm to determine the additive structure of indecomposable modules over ZCp, where Cp is the cyclic group of order a prime number p, and the p−pullback {Z→ Zp ← Z} of Z⊕Z.

Let Fq be the finite field with q elements, A := Fq[T ] and F := Fq(T ). Let φ be a Drinfeld A-module over F with trivial endomorphism ring. We prove analogues of the Erdös and Halberstam Theorems for φ. If φ has rank ≥ 3, we assume the validity of the Mumford-Tate Conjecture for φ. 1

In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.

We provide a complete classification of all tilting modules and tilting classes over almost perfect domains, which generalizes the classifications of tilting modules and tilting classes over Dedekind and 1-Gorenstein domains. Assuming the APD is Noetherian, a complete classification of all cotilting modules is obtained (as duals of the tilting ones).

We calculate the Grothendieck group K0(A), where A is an additive category, locally finite over a Dedekind ring and satisfying some additional conditions. The main examples are categories of modules algebras stable homotopy category SW CW-complexes. show that this direct sum free arising from localizations analogous to groups ideal classes maximal orders. As corollary, we obtain new simple proo...

This paper is a contribution to the theory of substructural logics. We introduce the notions of (MP)-based and almost (MP)-based logics (w.r.t. a special set of formulae D), which leads to an alternative proof of the well-known forms of the local deduction theorems for prominent substructural logics (FL, FLe, FLew , etc.). Roughly speaking, we decompose the proof of the local deduction theorem ...