TROPICAL ALGEBRAIC SETS, IDEALS AND AN ALGEBRAIC NULLSTELLENSATZ
نویسندگان
چکیده
منابع مشابه
Tropical Algebraic Sets, Ideals and an Algebraic Nullstellensatz
This paper introduces the foundations of the polynomial algebra and basic structures for algebraic geometry over the extended tropical semiring. Our development, which includes the tropical version for the fundamental theorem of algebra, leads to the reduced polynomial semiring – a structure that provides a basis for developing a tropical analogue to the classical theory of commutative algebra....
متن کاملTropical Varieties, Ideals and an Algebraic Nullstellensatz
The objective of this paper is to introduce the fundamental algebro-geometric constructions over the extended tropical semi-ring. The study of tropical varieties, co-varieties and ideals over this extension eventually yields the theorem of the weak tropical Nullstellensatz and gives an algebraic interpretation of the tropical Nullstellensatz.
متن کاملAlgebraic and topological aspects of quasi-prime ideals
In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...
متن کاملToric Ideals in Algebraic Statistics Toric Ideals in Algebraic Statistics
Toric Ideals in Algebraic Statistics
متن کاملAlgebraic Models of Sets and Classes in Categories of Ideals
We introduce a new sheaf-theoretic construction called the ideal completion of a category and investigate its logical properties. We show that it satisfies the axioms for a category of classes in the sense of Joyal and Moerdijk [17], so that the tools of algebraic set theory can be applied to produce models of various elementary set theories. These results are then used to prove the conservativ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2008
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196708004779