Certain generalizations of Boolean rings
Let and be two pointed sets. Given a family of three maps , this family provides an adequate decomposition of as the orthogonal disjoint union of well-described -invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak -algebras.
Let be a division ring finite dimensional over its center . The goal of this paper is to prove that for any positive integer there exists the th multiplicative derived subgroup such that is a maximal subfield of . We also show that a single depth- iterated additive commutator would generate a maximal subfield of
We give some sufficient and necessary conditions for an element in a ring to be an EP element, partial isometry, normal EP element and strongly EP element by using solutions of certain equations.