Arithmetic of additively reduced monoid semidomains

The term semidomain refers to a subset S of an integral domain R , in which the pairs ( S , + ) and ( S , · ) are semigroups with identities. If S contains no additive inverses except 0, we say that S is additively reduced. By taking polynomial expressions with coefficients in S and exponents in a torsion-free monoid M , we obtain the additively reduced monoid semidomain S [ M ]. In this paper, we investigate the factorization properties of such semidomains, providing necessary and sufficient conditions for them to be bounded factorization semidomains, finite factorization semidomains, and unique factorization semidomains. We also identify large classes of semidomains with full and infinite elasticity. Throughout the paper, we present examples to help elucidate the arithmetic of additively reduced monoid semidomains.