Explicit constructions of extractors and expanders
For generator of the multiplicative group of the field , the discrete logarithm of an element of the field to the base , is that integer , . The -ary digits which represent can be described with extremely simple polynomial forms.
This paper aims at the study of the notions of periodic, UU and semiclean properties in various context of commutative rings such as trivial ring extensions, amalgamations and pullbacks. The results obtained provide new original classes of rings subject to various ring theoretic properties.