Normalization of rings

Normalization of rings

We present a new algorithm to compute the integral closure of a reduced Noetherian ring in its total ring of fractions. We proceed, as in the classical case, by constructing an ascending chain of endomorphism rings of test ideals. However, our approach avoids the increasing complexity when enlarging the rings by doing most computations over the original ring. A modification, applicable in posit...

Noetherian rings without finite normalization

A number of examples and constructions of local Noetherian domains without finite normalization have been exhibited over the last seventy-five years. We discuss some of these examples, as well as the theory behind them.

Differential Polynomial Rings of Triangular Matrix Rings

Sociological Study of the Determinants of Normalization of Research Misbehavior

Nowadays, promoting academic loyalty and ethics and coping with research misbehavior, including plagiarism, forgery and misrepresentation have become an important part of the university mission, since the normalization of research misconduct undermines the integrity and loyalty of science, the link between science, society, industry, and damages the reputation of scientific institutions. Accord...

cDNA Microarray Data Normalization