Ecuaciones lineales y anillos conmutativos.
We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.
We study ADC quadratic forms and Euclidean quadratic forms over the integers, obtaining complete classification results in the positive case.