 About 2,820 results  books.google.com M. Hazewinkel MSC1991: 14Hxx FLOOR FUNCTION, entier function, greatest
integer function, integral part function  The ... of a localglobal principle in
commutative algebra (cf. also Localglobal principles for large rings of algebraic
integers; ... 

 books.google.com Relations with Arithmetic and Algebraic Geometry : Workshop on Hilbert's Tenth
Problem : Relations with Arithmetic and Algebraic Geometry, November 25,
1999, Ghent University, ... [JR98] M. Jarden and A. Razon, Rumely's local global
principle for algebraic PS C fields over rings, Trans. ... [Raz95] A. Razon,
Primitive recursive decidability for large rings of algebraic integers, Phd thesis,
Tel Aviv, 1995. 

 books.google.com global. fields. of. infinite. degree. Since HTP clearly becomes decidable over the
field of all algebraic numbers (the algebraic ... one could use such a curve to give
a definition of Z over the ring of algebraic integers of this totally real infinite
extension. ... The proof relied on what became known as Rumely's localglobal
principle, stating that a variety has a smooth integral point in the algebraic
closure of Q if ... 

 books.google.com However, quadratic forms were considered usually over the integers or over the
fields R and C. The equivalence problem over integers ... Thus, Hilbert asks for
solution of the representation problem over algebraic number fields and over
rings of algebraic integers. ... Hilbert's result is a prototype of a local–global
principle: the equation ax2 + by2 = 1 is solvable in the field K if and only if it is
solvable in all ... 

 books.google.com (We include the "infinite prime"; for example, Qoo is considered to be R.)
Unfortunately, good localglobal principles are hard to ... one to determine
precisely how far a ring of algebraic integers is from being a UFD, in terms of the
class number. 

 books.google.com G. Cornelissen, T. Pheidas, K. Zahidi, Divisionample sets and the Diophantine
problem for rings of integers. ... L. Darnière, Decidability and localglobal
principles, in Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic
Geometry. 

 books.google.com 18. van den Dries, L., Elimination theory for the ring of algebraic integers, J.
Reine Angew. Math., 388, 189205, 1988. 19. van den Dries, L. and Macintyre, A.
, The logic of Rumely's local.global principle, J. Reine Angew. Math., 407, 3356,
... 

 books.google.com See also GLOBAL, LOCAL FIELD, LOCAL RING, MANIFOLD, TOPOLOGICAL
SPACE Local Cell The POLYHEDRON resulting from letting ... about the
equation in a GLOBAL FIELD, such as the rational numbers or a NUMBER FIELD
(e.g., the HASSE PRINCIPLE). Local class field theory is termed "local" because
the local fields are LOCALIZED at a PRIME IDEAL in the RING of ALGEBRAIC
INTEGERS. 

 books.google.com Each of these two distributive lattices has a basis whose elements are indexed by
the ring elements, and thus live at the very type level of the ... to mention only
three of them, there is: the ring Z of integers, the field Q of rational numbers, and
the field of algebraic numbers. Localglobal principles With a pointfree
representation of the Zariski spectrum such as Joyal's, also the localglobal
principles vital for ... 

 books.google.com Key words and phrases: (near) Boolean family of valuation rings, (near) regularly
 Priifer ring, localglobal principle. ... in connection with the remarkable Rumely's
proof of a localglobal principle for the ring of algebraic integers [24] and some ... 

 