Let V (resp. D) be a valuation domain (resp. SFT Prüfer domain), I a proper ideal, and V̂ (resp. D̂) be the I-adic completion of V (resp. D). We show that (1) V̂ is a valuation domain, (2) Krull dimension of V̂ = dimV I+1 if I is not idempotent, V̂ ∼= V I if I is idempotent, (3) dim D̂ = dimD I + 1, (4) D̂ is an SFT Prüfer ring, and (5) D̂ is a catenarian ring. Throughout this paper, all rings are assu...

Introduction 0.1. Let X be a scheme, reduced and separated, of finite type over Z. For p a prime number, one may consider the set X(Z p) of its Z p-rational points. For every n in N, there is a natural map π n : X(Z p) → X(Z/p n+1) assigning to a Z p-rational point its class modulo p n+1. The image Y n,p of X(Z p) by π n is exactly the set of Z/p n+1-rational points which can be lifted to Z p-r...

It is very well known that additional algebraic structure can give advantages for coding applications. For example, all cyclic error-correcting codes are principal ideals in the group algebras of cyclic groups (see the survey [4] and the books [3, 5, 6, 7]). Serious attention in the literature has been devoted to considering properties of ideals in various ring constructions essential from the ...

o r g a n i z a t i o n s i n a s u p p l y c h a i n a r e i n d e p e n d e n t e n t i t i e s. a l t h o u g h a c o m p l e t e l y i n t e g r a t e d s o l u t i o n m a y r e s u l t i n o p t i m a l s y s t e m p e r f o r m a n c e, s u p p l y c h a i n m e m b e r s a r e i n t e r e s t e d i n o p t i m i z i n g t h e i r o w n o b j e c t i v e r a t h e r t h a n t h a t o f t...

The multiplicative structure of the cohomology ring of the moduli space of stable rank 2 bundles on a smooth projective curve is computed. INTRODUCTION Let C be a complete smooth curve of genus g ≥ 2 over the field of complex numbers C. Consider the moduli space N of stable rank 2 vector bundles on C with fixed determinant L of odd degree 2k− 1 . Then N is a smooth projective variety of dimensi...

whose domain is the symplectic bordism ring of V. L. Ginzburg [2]. As Ginzburg proved σ to be injective, this establishes it to be an isomorphism, a result first proved by J. Morava [3] by a more topological argument. We also make some observations on the associated homology theory. For the benefit of topologists, we remark that the notion of manifold with symplectic structure is distinct from ...

K S A H A , * K N R AO , * V N S E H G A L , t S G A D I , t v K J A I N§ & A K C H A K R A BA R T Y� * Vallabhbhai Patel Chest Institute, University of Delhi, Delhi1 10 007; t Maulana A zad Medical College and associa ted LNJPN and GB Pant Hospitals , New Delhi; :j: Hindusthan Copper Complex Mines Hospital, Mosabani 832 104; § Department of Dermatology, Medical College Hospital, Roh tak 124 00...

DISSERTATION zur Erlangung des akademischen Grades doctor rerum naturalium Dedicated to the memory of KARIN GATERMANN Table 1: List of mathematical symbols C field of complex numbers R field of real numbers Z ring of integer numbers C[x] ring of polynomials with coefficients in the field of complex numbers I ideal I def, tor deformed toric ideal V (I) variety of an ideal V (I def, tor) variety ...