About 2,820 results
|M. Hazewinkel MSC1991: 14Hxx FLOOR FUNCTION, entier function, greatest |
integer function, integral part function - The ... of a local-global principle in
commutative algebra (cf. also Local-global principles for large rings of algebraic
|Relations with Arithmetic and Algebraic Geometry : Workshop on Hilbert's Tenth |
Problem : Relations with Arithmetic and Algebraic Geometry, November 2-5,
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.
|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 local-global
principle, stating that a variety has a smooth integral point in the algebraic
closure of Q if ...
|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 ...
|(We include the "infinite prime"; for example, Qoo is considered to be R.) |
Unfortunately, good local-global principles are hard to ... one to determine
precisely how far a ring of algebraic integers is from being a UFD, in terms of the
|18. van den Dries, L., Elimination theory for the ring of algebraic integers, J. |
Reine Angew. Math., 388, 189-205, 1988. 19. van den Dries, L. and Macintyre, A.
, The logic of Rumely's local.global principle, J. Reine Angew. Math., 407, 33-56,
|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
|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. Local-global principles With a point-free
representation of the Zariski spectrum such as Joyal's, also the local-global
principles vital for ...
|Key words and phrases: (near) Boolean family of valuation rings, (near) regularly|
- Priifer ring, local-global principle. ... in connection with the remarkable Rumely's
proof of a local-global principle for the ring of algebraic integers  and some ...