Let k be an algebraic number eld with maximal order o k and let m 0 be an ideal of o k. We develop an algorithm for the computation of the multiplicative group (o k =m 0) of the residue class ring o k =m 0. It is applied to the computation of the ray class group Cl m k modulo m = m 0 m 1 , where m 1 denotes a formal product of real innnite places, and also to the computation of the conductor of...

a presentation of M , where F is a free module of arbitrary rank. Let U denote the matrix (with n rows but possibly infinitely many columns) representing φ with respect to some fixed bases for F and An. For t ≥ 1 we let It(φ) denote the ideal of A generated by all t-sized minors U . (This ideal is independent of the choice of bases.) By convention, It(φ) = R for t ≤ 0 and It(φ) = 0 if t exceeds...

We determine all nonquadratic imaginary cyclic number fields K of 2-power degrees with ideal class groups of exponents < 2, i.e., with ideal class groups such that the square of each ideal class is the principal class, i.e., such that the ideal class groups are isomorphic to some (Z/2Z)m , m > 0. There are 38 such number fields: 33 of them are quartic ones (see Theorem 13), 4 of them are octic ...

The reduction number r(A) of a standard graded algebra A is the least integer k such that there exists a minimal reduction J of the homogeneous maximal ideal m of A such that J m = m. Vasconcelos conjectured that r(R/I) ≤ r(R/ in(I)) where in(I) is the initial ideal of an ideal I in a polynomial ring R with respect to a term order. The goal of this note is to prove the conjecture. 1. Reduction ...

Given a module M over a ring R that has a grading by a semigroup Q, we present a spectral sequence that computes the local cohomology H I(M) at any graded ideal I in terms of Ext modules. We use this method to obtain finiteness results for the local cohomology of graded modules over semigroup rings. In particular we prove that for a semigroup Q whose saturation Q is simplicial, and a finitely g...

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, i...

This work introduces the concept of an M-complete approximate identity (M-cai) for a given operator subspace X of an operator space Y. M-cai's generalize central approximate identities in ideals in C *-algebras, for it is proved that if X admits an M-cai in Y , then X is a complete M-ideal in Y. It is proved, using " special " M-cai's, that if J is a nuclear ideal in a C *-algebra A, then J is ...

BACKGROUND Recent studies have shown that body image perception is an important factor in weight control and may be influenced by culture and ethnicity. The aim of the present study was to assess the relationship between immigrant status of the mother and weight status and body image perception of the child. METHODS In total, 2706 schoolchildren (1405 boys and 1301 girls) aged 8-9 years and t...

The main object of this note is to study the conormal module M and the computation of the second symbolic power ḡ of an ideal ḡ in the residue ring O/h of a polynomial ring O over a field of characteristic zero. The torsion part T (M) of M and the torsion free module M/T (M) are expressed by the primitive ideal of g relative to h. Two characterizations for M/T (M) to be free are proved. Some im...