منابع مشابه
Strongly Noetherian rings and constructive ideal theory
We give a new constructive definition for Noetherian rings. It has a very concrete statement and is nevertheless strong enough to prove constructively the termination of algorithms involving “trees of ideals”. The efficiency of such algorithms (at least for providing clear and intuitive constructive proofs) is illustrated in a section about Lasker–Noether rings: we give constructive proofs for ...
متن کاملOn the Structure and Ideal Theory of Complete Local Rings
Introduction. The concept of a local ring was introduced by Krull [7](1), who defined such a ring as a commutative ring 9î in which every ideal has a finite basis and in which the set m of all non-units is an ideal, necessarily maximal. He proved that the intersection of all the powers of m is the zero ideal. If the powers of m are introduced as a system of neighborhoods of zero, then 3Î thus b...
متن کاملComputational ideal theory in nitely generated extension rings
Since Buchberger introduced the theory of Gr obner bases in 1965 it has become an important tool in constructive algebra and, nowadays, Buchberger’s method is fundamental for many algorithms in the theory of polynomial ideals and algebraic geometry. Motivated by the results in polynomial rings a lot of possibilities to generalize the ideas to other types of rings have been investigated. The pe...
متن کاملComputational ideal theory in finitely generated extension rings
One of the most general extensions of Buchberger's theory of Grobner bases is the concept of graded structures due to Robbiano and Mora. But in order to obtain algorithmic solutions for the computation of Gr obner bases it needs additional computability assumptions. In this paper we introduce natural graded structures of nitely generated extension rings and present subclasses of such structur...
متن کاملA Formula for Ideal Lattices of General Commutative Rings
Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1960
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(60)50060-6