Contributions to Ideal Theory in General Rings

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 ...

Contributions of ideal observer theory to vision research

An ideal observer is a hypothetical device that performs optimally in a perceptual task given the available information. The theory of ideal observers has proven to be a powerful and useful tool in vision research, which has been applied to a wide range of problems. Here I first summarize the basic concepts and logic of ideal observer analysis and then briefly describe applications in a number ...

Emmy Noether’s contributions to the theory of group rings

Computational 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...

Computational 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...