Main-group element Main-group element In chemistry and atomic physics, the main group is the group of elements whose lightest members are represented by helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, and fluorine as arranged in the periodic table of the elements. The main group includes the elements (except hydrogen, which is sometimes not included) in groups 1 and 2 (s-block), and groups 13 to 18 (p-block). The s-block elements are primarily characterised by one main oxidation state, and the p-block elements, when they have multiple oxidation states, often have common oxidation states separated by two units. Main-group elements (with some of the
Quasiregular element if and only if it satisfies the product-star Conway axiom. Quasiregular semirings appear in s, a generalization of the shortest path problem. Quasiregular element In mathematics, specifically ring theory, the notion of quasiregularity provides a computationally convenient way to work with the Jacobson radical of a ring. Intuitively, quasiregularity captures what it means for an element of a ring to be "bad"; that is, have undesirable properties. Although a "bad element" is necessarily quasiregular, quasiregular elements need not be "bad", in a rather vague sense. In this article, we primarily concern ourselves with the notion of quasiregularity for unital rings.