In this thesis we investigate the extension of certain theorems
of additive number theory to three algebraic systems. A generalization
of a theorem by Cauchy and Davenport on the cardinality of the
sum of two sets of residue classes is given. We obtain and compare
estimates for the order of...
Allen Freedman defined a density space to be the ordered pair
(S,𝓕) where S is a certain kind of semigroup called an s-set and 𝓕
is a special type of family of finite subsets of S called a fundamental
family on S. Several properties for density spaces are
obtained, and...