In this paper, we study the atomic structure of certain classes of semigroup algebras whose sets of exponents are additive submonoids of rational numbers. When studying the atomicity of integral domains, the building blocks by excellence are the irreducible elements. Here we start by extending the Gauss's Lemma and the Eisenstein's Criterion from polynomial rings to semigroup rings with rational exponents. Then we prove that semigroup algebras whose exponent sets are submonoids of $\langle 1/p \mid p \ \text{ is prime} \rangle$ are atomic. Next, for every algebraic closed field $F$, we exhibit a class of Bezout semigroup algebras over $F$ with rational exponents whose members are antimatter, i.e., contain no atoms. In addition, we use a class of root-closed additive submonoids of rationals to construct another class of antimatter semigroup algebras over any perfect field of finite characteristic. Finally, we characterize the irreducible elements of semigroup algebras whose exponent sem 查看全文>>